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Transformations of polynomial ensemblesJan 22 2015Jan 30 2015A polynomial ensemble is a probability density function for the position of $n$ real particles of the form $\frac{1}{Z_n} \, \prod_{j<k} (x_k-x_j) \, \det \left[ f_k (x_j) \right]_{j,k=1}^n$, for certain functions $f_1, \ldots, f_n$. Such ensembles appear ... More

Multiple orthogonal polynomial ensemblesFeb 06 2009Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we introduce the ... More

A Vector Equilibrium Problem for Muttalib-Borodin Biorthogonal EnsemblesApr 11 2016Jul 05 2016The Muttalib-Borodin biorthogonal ensemble is a joint density function for $n$ particles on the positive real line that depends on a parameter $\theta$. There is an equilibrium problem that describes the large $n$ behavior. We show that for rational values ... More

Multiple orthogonal polynomials in random matrix theoryApr 06 2010Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point processes ... More

Orthogonal polynomials in the normal matrix model with a cubic potentialJun 30 2011We consider the normal matrix model with a cubic potential. The model is ill-defined, and in order to reguralize it, Elbau and Felder introduced a model with a cut-off and corresponding system of orthogonal polynomials with respect to a varying exponential ... More

The supercritical regime in the normal matrix model with cubic potentialDec 24 2014Dec 27 2014The normal matrix model with a cubic potential is ill-defined and it develops a critical behavior in finite time. We follow the approach of Bleher and Kuijlaars to reformulate the model in terms of orthogonal polynomials with respect to a Hermitian form. ... More

Painleve IV asymptotics for orthogonal polynomials with respect to a modified Laguerre weightApr 16 2008Jul 08 2008We study polynomials that are orthogonal with respect to the modified Laguerre weight $z^{-n + \nu} e^{-Nz} (z-1)^{2b}$ in the limit where $n, N \to \infty$ with $N/n \to 1$ and $\nu$ is a fixed number in $\mathbb{R} \setminus \mathbb{N}_0$. With the ... More

A graph-based equilibrium problem for the limiting distribution of non-intersecting Brownian motions at low temperatureJul 14 2009We consider n non-intersecting Brownian motion paths with p prescribed starting positions at time t=0 and q prescribed ending positions at time t=1. The positions of the paths at any intermediate time are a determinantal point process, which in the case ... More

The normal matrix model with a monomial potential, a vector equilibrium problem, and multiple orthogonal polynomials on a starJan 10 2014Jan 16 2015We investigate the asymptotic behavior of a family of multiple orthogonal polynomials that is naturally linked with the normal matrix model with a monomial potential of arbitrary degree $d+1$. The polynomials that we investigate are multiple orthogonal ... More

Large n limit of Gaussian random matrices with external source, Part III: Double scaling limitFeb 28 2006We consider the double scaling limit in the random matrix ensemble with an external source $\frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM$ defined on $n\times n$ Hermitian matrices, where $A$ is a diagonal matrix with two eigenvalues $\pm a$ of equal multiplicities. ... More

Exceptional Laguerre polynomialsAug 10 2017Jan 23 2018The aim of this paper is to present the construction of exceptional Laguerre polynomials in a systematic way, and to provide new asymptotic results on the location of the zeros. To describe the exceptional Laguerre polynomials we associate them with two ... More

Singular values of products of random matrices and polynomial ensemblesApr 23 2014Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M complex Ginibre matrices are distributed according to a determinantal point process. We introduce the notion of a polynomial ensemble and show how their result ... More

Universality in the two matrix model: a Riemann-Hilbert steepest descent analysisJul 30 2008The eigenvalue statistics of a pair $(M_1,M_2)$ of $n\times n$ Hermitian matrices taken random with respect to the measure $$\frac{1}{Z_n}\exp\big(-n\Tr (V(M_1)+W(M_2)-\tau M_1M_2)\big) {\rm d}M_1 {\rm d} M_2 $$ can be described in terms of two families ... More

The two periodic Aztec diamond and matrix valued orthogonal polynomialsDec 15 2017Jan 29 2019We analyze domino tilings of the two-periodic Aztec diamond by means of matrix valued orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non-intersecting path model with periodic transition matrices. In a more general ... More

Large Deviations for a Non-Centered Wishart MatrixApr 27 2012Mar 12 2013We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic potential theory, ... More

Integral representations for multiple Hermite and multiple Laguerre polynomialsJun 30 2004We give integral representations for multiple Hermite and multiple Hermite polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.

Universality of the double scaling limit in random matrix modelsJan 31 2005We study unitary random matrix ensembles in the critical case where the limiting mean eigenvalue density vanishes quadratically at an interior point of the support. We establish universality of the limits of the eigenvalue correlation kernel at such a ... More

A phase transition for non-intersecting Brownian motions, and the Painleve II equationSep 05 2008We consider n non-intersecting Brownian motions with two fixed starting positions and two fixed ending positions in the large n limit. We show that in case of 'large separation' between the endpoints, the particles are asymptotically distributed in two ... More

Double scaling limit for modified Jacobi-Angelesco polynomialsFeb 07 2011We consider multiple orthogonal polynomials with respect to two modified Jacobi weights on touching intervals [a,0] and [0,1], with a < 0, and study a transition that occurs at a = -1. The transition is studied in a double scaling limit, where we let ... More

Large n limit of Gaussian random matrices with external source, part IFeb 16 2004Feb 20 2004We consider the random matrix ensemble with an external source \[ \frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM \] defined on $n\times n$ Hermitian matrices, where $A$ is a diagonal matrix with only two eigenvalues $\pm a$ of equal multiplicity. For the case ... More

Universality for conditional measures of the sine point processMar 07 2017Mar 21 2019The sine process is a rigid point process on the real line, which means that for almost all configurations $X$, the number of points in an interval $I = [-R,R]$ is determined by the points of $X$ outside of $I$. In addition, the points in $I$ are an orthogonal ... More

Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limitsAug 05 2013Dec 23 2013Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation kernel that ... More

Weakly Admissible Vector Equilibrium ProblemsOct 31 2011Apr 23 2012We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for such vector ... More

An equilibrium problem for the limiting eigenvalue distribution of banded Toeplitz matricesApr 03 2007We study the limiting eigenvalue distribution of $n\times n$ banded Toeplitz matrices as $n\to \infty$. From classical results of Schmidt-Spitzer and Hirschman it is known that the eigenvalues accumulate on a special curve in the complex plane and the ... More

Universality in unitary random matrix ensembles when the soft edge meets the hard edgeJan 02 2007Jun 22 2007Unitary random matrix ensembles Z_{n,N}^{-1} (\det M)^alpha exp(-N Tr V(M)) dM defined on positive definite matrices M, where alpha > -1 and V is real analytic, have a hard edge at 0. The equilibrium measure associated with V typically vanishes like a ... More

Spherical functions approach to sums of random Hermitian matricesNov 27 2016We present an approach to sums of random Hermitian matrices via the theory of spherical functions for the Gelfand pair $(\mathrm{U}(n) \ltimes \mathrm{Herm}(n), \mathrm{U}(n))$. It is inspired by a similar approach of Kieburg and K\"osters for products ... More

A vector equilibrium problem for the two-matrix model in the quartic/quadratic caseJul 19 2010We consider the two sequences of biorthogonal polynomials (p_{k,n})_k and (q_{k,n})_k related to the Hermitian two-matrix model with potentials V(x) = x^2/2 and W(y) = y^4/4 + ty^2. From an asymptotic analysis of the coefficients in the recurrence relation ... More

A numerical method for oscillatory integrals with coalescing saddle pointsJun 18 2018The value of a highly oscillatory integral is typically determined asymptotically by the behaviour of the integrand near a small number of critical points. These include the endpoints of the integration domain and the so-called stationary points or saddle ... More

Correlation kernels for sums and products of random matricesMay 04 2015Sep 03 2015Let $X$ be a random matrix whose squared singular value density is a polynomial ensemble. We derive double contour integral formulas for the correlation kernels of the squared singular values of $GX$ and $TX$, where $G$ is a complex Ginibre matrix and ... More

A numerical method for oscillatory integrals with coalescing saddle pointsJun 18 2018Jun 24 2019The value of a highly oscillatory integral is typically determined asymptotically by the behaviour of the integrand near a small number of critical points. These include the endpoints of the integration domain and the so-called stationary points or saddle ... More

Multiple Meixner-Pollaczek polynomials and the six-vertex modelJan 15 2011Feb 21 2011We study multiple orthogonal polynomials of Meixner-Pollaczek type with respect to a symmetric system of two orthogonality measures. Our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to ... More

Asymptotic analysis of the two matrix model with a quartic potentialSep 29 2012We give a summary of the recent progress made by the authors and collaborators on the asymptotic analysis of the two matrix model with a quartic potential. The paper also contains a list of open problems.

Asymptotic behavior and zero distribution of polynomials orthogonal with respect to Bessel functionsJun 04 2014We consider polynomials $P_n$ orthogonal with respect to the weight $J_{\nu}$ on $[0,\infty)$, where $J_{\nu}$ is the Bessel function of order $\nu$. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for ... More

Propagation of singular behavior for Gaussian perturbations of random matricesAug 20 2016We study the asymptotic behavior of the eigenvalues of Gaussian perturbations of large Hermitian random matrices for which the limiting eigenvalue density vanishes at a singular interior point or vanishes faster than a square root at a singular edge point. ... More

Large $n$ limit of Gaussian random matrices with external source, part IIAug 25 2004We continue the study of the Hermitian random matrix ensemble with external source $\frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM$ where $A$ has two distinct eigenvalues $\pm a$ of equal multiplicity. This model exhibits a phase transition for the value $a=1$, ... More

Singular value statistics of matrix products with truncated unitary matricesJan 16 2015We prove that the squared singular values of a fixed matrix multiplied with a truncation of a Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is applied to a multiplication of a truncated unitary matrix with a random ... More

Non-intersecting squared Bessel paths with one positive starting and ending pointMay 12 2011May 13 2011We consider a model of $n$ non-intersecting squared Bessel processes with one starting point $a>0$ at time t=0 and one ending point $b>0$ at time $t=T$. After proper scaling, the paths fill out a region in the $tx$-plane. Depending on the value of the ... More

The Hermitian two matrix model with an even quartic potentialOct 20 2010We consider the two matrix model with an even quartic potential W(y)=y^4/4+alpha y^2/2 and an even polynomial potential V(x). The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues ... More

Critical behavior of non-intersecting Brownian motions at a tacnodeSep 13 2010We study a model of $n$ one-dimensional non-intersecting Brownian motions with two prescribed starting points at time $t=0$ and two prescribed ending points at time $t=1$ in a critical regime where the paths fill two tangent ellipses in the time-space ... More

Random matrix model with external source and a constrained vector equilibrium problemJan 08 2010We consider the random matrix model with external source, in case where the potential V(x) is an even polynomial and the external source has two eigenvalues a, -a of equal multiplicity. We show that the limiting mean eigenvalue distribution of this model ... More

A periodic hexagon tiling model and non-Hermitian orthogonal polynomialsJul 04 2019We study a one-parameter family of probability measures on lozenge tilings of large regular hexagons that interpolates between the uniform measure on all possible tilings and a particular fully frozen tiling. The description of the asymptotic behavior ... More

An equilibrium problem on the sphere with two equal chargesJul 10 2019We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by two equal point charges. The support of the equilibrium measure is known as the droplet. Brauchart et al. showed that the complement of the ... More

The tacnode Riemann-Hilbert problemApr 23 2013The tacnode Riemann-Hilbert problem is a 4 x 4 matrix valued RH problem that appears in the description of the local behavior of two touching groups of non-intersecting Brownian motions. The same RH problem was also found by Duits and Geudens to describe ... More

UniversalityMar 30 2011Apr 02 2011Universality of eigenvalue spacings is one of the basic characteristics of random matrices. We give the precise meaning of universality and discuss the standard universality classes (sine, Airy, Bessel) and their appearance in unitary, orthogonal, and ... More

Painleve I asymptotics for orthogonal polynomials with respect to a varying quartic weightMay 08 2006We study polynomials that are orthogonal with respect to a varying quartic weight \exp(-N(x^2/2+tx^4/4)) for t<0, where the orthogonality takes place on certain contours in the complex plane. Inspired by developments in 2D quantum gravity, Fokas, Its, ... More

Universality for eigenvalue correlations from the modified Jacobi unitary ensembleApr 02 2002The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the edge in terms ... More

S-curves in Polynomial External FieldsNov 27 2013Apr 01 2014Curves in the complex plane that satisfy the S-property were first introduced by Stahl and they were further studied by Gonchar and Rakhmanov in the 1980s. Rakhmanov recently showed the existence of curves with the S-property in a harmonic external field ... More

The global parametrix in the Riemann-Hilbert steepest descent analysis for orthogonal polynomialsSep 30 2009Jul 28 2010In the application of the Deift-Zhou steepest descent method to the Riemann-Hilbert problem for orthogonal polynomials, a model Riemann-Hilbert problem that appears in the multi-cut case is solved with the use of hyperelliptic theta functions. We present ... More

A Christoffel-Darboux formula for multiple orthogonal polynomialsFeb 03 2004Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a Christoffel-Darboux formula for this ... More

Critical behavior in Angelesco ensemblesMar 13 2012We consider Angelesco ensembles with respect to two modified Jacobi weights on touching intervals [a,0] and [0,1], for a < 0. As a \to -1 the particles around 0 experience a phase transition. This transition is studied in a double scaling limit, where ... More

Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motionsNov 18 2005We present a generalization of multiple orthogonal polynomials of type I and type II, which we call multiple orthogonal polynomials of mixed type. Some basic properties are formulated, and a Riemann-Hilbert problem for the multiple orthogonal polynomials ... More

Universality for eigenvalue correlations at the origin of the spectrumMay 22 2003Jun 25 2003We establish universality of local eigenvalue correlations in unitary random matrix ensembles (1/Z_n) |\det M|^{2\alpha} e^{-n\tr V(M)} dM near the origin of the spectrum. If V is even, and if the recurrence coefficients of the orthogonal polynomials ... More

Random matrices with external source and multiple orthogonal polynomialsJul 28 2003We show that the average characteristic polynomial P_n(z) = E [\det(zI-M)] of the random Hermitian matrix ensemble Z_n^{-1} \exp(-Tr(V(M)-AM))dM is characterized by multiple orthogonality conditions that depend on the eigenvalues of the external source ... More

Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel pathsNov 19 2009In this paper we consider the model of $n$ non-intersecting squared Bessel processes with parameter $\alpha$, in the confluent case where all particles start, at time $t=0$, at the same positive value $x=a$, remain positive, and end, at time $T=t$, at ... More

Strong asymptotics for Jacobi polynomials with varying nonstandard parametersSep 27 2003Jan 10 2004Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$ \lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B, $$ with $A$ and $B$ ... More

Zeros of exceptional Hermite polynomialsDec 19 2014We study the zeros of exceptional Hermite polynomials associated with an even partition $\lambda$. We prove several conjectures regarding the asymptotic behavior of both the regular (real) and the exceptional (complex) zeros. The real zeros are distributed ... More

On Separation of Minimal Riesz Energy Points on Spheres in Euclidean SpacesMar 27 2005For the unit sphere S^d in Euclidean space R^(d+1), we show that for d-1<s<d and any N>1, discrete N-point minimal Riesz s-energy configurations are well separated in the sense that the minimal distance between any pair of distinct points in such a configuration ... More

Asymptotics of non-intersecting Brownian motions and a 4 x 4 Riemann-Hilbert problemJan 31 2007We consider n one-dimensional Brownian motions, such that n/2 Brownian motions start at time t=0 in the starting point a and end at time t=1 in the endpoint b and the other n/2 Brownian motions start at time t=0 at the point -a and end at time t=1 in ... More

Zero distribution of complex orthogonal polynomials with respect to exponential weightsDec 16 2013We study the limiting zero distribution of orthogonal polynomials with respect to some particular exponential weights exp(-nV(z)) along contours in the complex plane. We are especially interested in the question under which circumstances the zeros of ... More

The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weightsAug 29 2007Sep 24 2007We consider orthogonal polynomials $\{p_{n,N}(x)\}_{n=0}^{\infty}$ on the real line with respect to a weight $w(x)=e^{-NV(x)}$ and in particular the asymptotic behaviour of the coefficients $a_{n,N}$ and $b_{n,N}$ in the three term recurrence $x \pi_{n,N}(x) ... More

Non-intersecting squared Bessel paths: critical time and double scaling limitNov 04 2010We consider the double scaling limit for a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t=0$ at the same positive value $x=a$, remain positive, and are conditioned to end at time $t=1$ at $x=0$. ... More

Asymptotics for Hermite-Pade rational approximants for two analytic functions with separated pairs of branch points (case of genus 0)Aug 07 2007We investigate the asymptotic behavior for type II Hermite-Pade approximation to two functions, where each function has two branch points and the pairs of branch points are separated. We give a classification of the cases such that the limiting counting ... More

Riemann--Hilbert analysis for Laguerre polynomials with large negative parameterApr 19 2002We study the asymptotic behavior of Laguerre polynomials $L_n^{(\alpha_n)}(nz)$ as $n \to \infty$, where $\alpha_n$ is a sequence of negative parameters such that $-\alpha_n/n$ tends to a limit $A > 1$ as $n \to \infty$. These polynomials satisfy a non-hermitian ... More

Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomialsApr 11 2002We introduce a spectral transform for the finite relativistic Toda lattice (RTL) in generalized form. In the nonrelativistic case, Moser constructed a spectral transform from the spectral theory of symmetric Jacobi matrices. Here we use a non-symmetric ... More

Orthogonality of Jacobi polynomials with general parametersJan 06 2003In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a Riemann surface. ... More

Multi-critical unitary random matrix ensembles and the general Painleve II equationAug 31 2005We study unitary random matrix ensembles of the form $Z_{n,N}^{-1} |\det M|^{2\alpha} e^{-N \Tr V(M)}dM$, where $\alpha>-1/2$ and $V$ is such that the limiting mean eigenvalue density for $n,N\to\infty$ and $n/N\to 1$ vanishes quadratically at the origin. ... More

Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadratureJan 13 2010In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of these polynomials are the nodes for complex Gaussian quadrature ... More

Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weightsDec 09 2007We study a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t = 0$ at the same positive value $x = a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. In the limit $n \to \infty$, ... More

Asymptotics for a special solution of the thirty fourth Painleve equationNov 24 2008In a previous paper we studied the double scaling limit of unitary random matrix ensembles of the form Z_{n,N}^{-1} |\det M|^{2\alpha} e^{-N \Tr V(M)} dM with \alpha > -1/2. The factor |\det M|^{2\alpha} induces critical eigenvalue behavior near the origin. ... More

Critical edge behavior in unitary random matrix ensembles and the thirty fourth Painleve transcendentApr 16 2007We describe a new universality class for unitary invariant random matrix ensembles. It arises in the double scaling limit of ensembles of random $n \times n$ Hermitian matrices $Z_{n,N}^{-1} |\det M|^{2\alpha} e^{-N \Tr V(M)} dM$ with $\alpha > -1/2$, ... More

A Riemann-Hilbert problem for biorthogonal polynomialsOct 14 2003We characterize the biorthogonal polynomials that appear in the theory of coupled random matrices via a Riemann-Hilbert problem. Our Riemann-Hilbert problem is different from the ones that were proposed recently by Ercolani and McLaughlin, Kapaev, and ... More

Asymptotic zero behavior of Laguerre polynomials with negative parameterMay 15 2002We consider Laguerre polynomials $L_n^{(\alpha_n)}(nz)$ with varying negative parameters $\alpha_n$, such that the limit $A = -\lim_n \alpha_n/n$ exists and belongs to $(0,1)$. For $A > 1$, it is known that the zeros accumulate along an open contour in ... More

Quadratic Hermite-Pade approximation to the exponential function: a Riemann-Hilbert approachFeb 28 2003We investigate the asymptotic behavior of the polynomials p, q, r of degrees n in type I Hermite-Pade approximation to the exponential function, defined by p(z)e^{-z}+q(z)+r(z)e^{z} = O(z^{3n+2}) as z -> 0. These polynomials are characterized by a Riemann-Hilbert ... More

More Mouldy Data: Another mycoplasma gene jumps the silicon barrier into the human genomeJun 21 2011The human genome sequence database contains DNA sequences very like those of mycoplasma molds. It appears such moulds infect not only molecular Biology laboratories but were picked up by experimenters from contaminated samples and inserted into GenBank ... More

Recurrence Relations for Exceptional Hermite PolynomialsJun 11 2015Jul 02 2015The bispectral anti-isomorphism is applied to differential operators involving elements of the stabilizer ring to produce explicit formulas for all difference operators having any of the Hermite exceptional orthogonal polynomials as eigenfunctions with ... More

Type II Hermite-Padé approximation to the exponential functionOct 13 2005We obtain strong and uniform asymptotics in every domain of the complex plane for the scaled polynomials $a (3nz)$, $b (3nz)$, and $c (3nz)$ where $a$, $b$, and $c$ are the type II Hermite-Pad\'e approximants to the exponential function of respective ... More

The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]Nov 23 2001Sep 01 2003We consider polynomials that are orthogonal on $[-1,1]$ with respect to a modified Jacobi weight $(1-x)^\alpha (1+x)^\beta h(x)$, with $\alpha,\beta>-1$ and $h$ real analytic and stricly positive on $[-1,1]$. We obtain full asymptotic expansions for the ... More

Locating the zeros of partial sums of exp(z) with Riemann-Hilbert methodsSep 08 2007In this paper we derive uniform asymptotic expansions for the partial sums of the exponential series. We indicate how this information will be used in a later publication to obtain full and explicitly computable asymptotic expansions with error bounds ... More

A pair potential that reproduces the shape of isochrones in molecular liquidsApr 19 2016Aug 18 2016Many liquids have curves (isomorphs) in their phase diagrams along which structure, dynamics, and some thermodynamic quantities are invariant in reduced units. A substantial part of their phase diagrams is thus effectively one dimensional. The shape of ... More

Scaling of the dynamics of flexible Lennard-Jones chainsJul 19 2013Aug 08 2014The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport ... More

Nonlinear State Space Model Identification Using a Regularized Basis Function ExpansionOct 02 2015This paper is concerned with black-box identification of nonlinear state space models. By using a basis function expansion within the state space model, we obtain a flexible structure. The model is identified using an expectation maximization approach, ... More

Computationally Efficient Bayesian Learning of Gaussian Process State Space ModelsJun 07 2015Apr 15 2016Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting ... More

Scaling of the dynamics of flexible Lennard-Jones chains. II. Effects of harmonic bondsAug 19 2015Nov 09 2015The previous paper [Veldhorst et al., J. Chem. Phys. 141, 054904 (2014)] demonstrated that the isomorph theory explains the scaling properties of a liquid of flexible chains consisting of ten Lennard-Jones particles connected by rigid bonds. We here investigate ... More

Invariants in the Yukawa system's thermodynamic phase diagramMay 25 2015Jun 30 2015This paper shows that several known properties of the Yukawa system can be derived from the isomorph theory, which applies to any system that has strong correlations between its virial and potential-energy equilibrium fluctuations. Such "Roskilde-simple" ... More

Assessment of the GW approximation using Hubbard chainsNov 13 1997We investigate the performance of the GW approximation by comparison to exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are examined, and we show ... More

Relativistic Resonances, Relativistic Gamow Vectors and Representations of the Poincare' SemigroupDec 22 1999The foundations of time asymmetric quantum theory are reviewed and are applied to the construction of relativistic Gamow vectors. Relativistic Gamow vectors are obtained from the resonance pole of the S-matrix and furnish an irreducible representation ... More

Stripe orientation in an anisotropic t-J modelFeb 28 2001The tilt pattern of the CuO_6 octahedra in the LTT phase of the cuprate superconductors leads to planar anisotropies for the exchange coupling and hopping integrals. Here, we show that these anisotropies provide a possible structural mechanism for the ... More

Spectra and total energies from self-consistent many-body perturbation theoryJun 09 1998With the aim of identifying universal trends, we compare fully self-consistent electronic spectra and total energies obtained from the GW approximation with those from an extended GWGamma scheme that includes a nontrivial vertex function and the fundamentally ... More

Irreversible Quantum Mechanics in the Neutral K-SystemMay 07 1997The neutral Kaon system is used to test the quantum theory of resonance scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with complex Hamiltonian is obtained by truncating the complex basis vector expansion of the exact theory ... More

Observation of an excess at 30 GeV in the opposite sign di-muon spectra of ${\rm Z} \to b\overline{ b} + {\rm X}$ events recorded by the ALEPH experiment at LEPOct 20 2016Apr 12 2018The re-analysis of the archived data recorded at the ${\rm Z}^{0}$ resonance by the ALEPH experiment at LEP during the years 1992-1995 shows an excess in the opposite sign di-muon mass spectra at 30.40 $\pm$ 0.46 GeV in events containing b quarks. The ... More

Most linear flows on $\mathbb{R}^d$ are BenfordJan 21 2015A necessary and sufficient condition ("exponential nonresonance") is established for every signal obtained from a linear flow on $\mathbb{R}^d$ by means of a linear observable to either vanish identically or else exhibit a strong form of Benford's Law ... More

Infinite Oracle Queries in Type-2 Machines (Extended Abstract)Jul 20 2009We define Oracle-Type-2-Machine capable of writing infinite oracle queries. In contrast to finite oracle queries, this extends the realm of oracle-computable functions into the discontinuous realm. Our definition is conservative; access to a computable ... More

Combinatorics of the basic stratumNov 14 2012We express the cohomology of the basic stratum of some unitary Shimura varieties associated to division algebras in terms of automorphic representations of the group in the Shimura datum.

Effective local compactness and the hyperspace of located setsMar 13 2019We revisit the definition of effective local compactness, and propose an approach that works for arbitrary countably-based spaces extending the previous work on computable metric spaces. We use this to show that effective local compactness suffices to ... More

Elementary geometric local-global principles for fieldsAug 19 2014We define and investigate a family of local-global principles for fields involving both orderings and p-valuations. This family contains the PAC, PRC and PpC fields and exhausts the class of pseudo classically closed fields. We show that the fields satisfying ... More

Subfields of ample fields I. Rational maps and definabilityNov 18 2008Pop proved that a smooth curve C over an ample field K that has a K-rational point has |K| many K-rational points. We strengthen this result by showing that there are |K| many K-rational points that do not lie in a given proper subfield, even after applying ... More

Parameterized Games and Parameterized AutomataSep 10 2018We introduce a way to parameterize automata and games on finite graphs with natural numbers. The parameters are accessed essentially by allowing counting down from the parameter value to 0 and branching depending on whether 0 has been reached. The main ... More

The Complexity of Iterated Strategy EliminationOct 27 2009Jan 20 2010We consider the computational complexity of the question whether a certain strategy can be removed from a game by means of iterated elimination of dominated strategies. In particular, we study the influence of different definitions of domination and of ... More

Optical conductivity of metals from first principlesSep 13 2011A computational method to obtain optical conductivities from first principles is presented. It exploits a relation between the conductivity and the complex dielectric function, which is constructed from the full electronic band structure within the random-phase ... More

Tableaux for the Lambek-Grishin calculusSep 16 2010Categorial type logics, pioneered by Lambek, seek a proof-theoretic understanding of natural language syntax by identifying categories with formulas and derivations with proofs. We typically observe an intuitionistic bias: a structural configuration of ... More