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Exact short-time height distribution in 1D KPZ equation with Brownian initial conditionMay 12 2017The early time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension, starting from a Brownian initial condition with a drift $w$, is studied using the exact Fredholm determinant representation. For large drift we recover the exact results ... More

Large fluctuations of the KPZ equation in a half-spaceApr 24 2018Jul 26 2018We investigate the short-time regime of the KPZ equation in $1+1$ dimensions and develop a unifying method to obtain the height distribution in this regime, valid whenever an exact solution exists in the form of a Fredholm Pfaffian or determinant. These ... More

Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-lineMay 14 2019We consider the Kardar-Parisi-Zhang (KPZ) for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential ... More

Linear statistics and pushed Coulomb gas at the edge of beta random matrices: four paths to large deviationsNov 01 2018The Airy$_\beta$ point process, $a_i \equiv N^{2/3} (\lambda_i-2)$, describes the eigenvalues $\lambda_i$ at the edge of the Gaussian $\beta$ ensembles of random matrices for large matrix size $N \to \infty$. We study the probability distribution function ... More

Simple derivation of the $(- λH)^{5/2}$ tail for the 1D KPZ equationFeb 23 2018We study the long-time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions for the Brownian and droplet initial conditions and present a simple derivation of the tail of the large deviations of the height on the negative side $\lambda ... More

Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-lineMay 14 2019May 17 2019We consider the Kardar-Parisi-Zhang (KPZ) for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential ... More

Systematic time expansion for the Kardar-Parisi-Zhang equation, linear statistics of the GUE at the edge and trapped fermionsAug 23 2018We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked against a ... More

Distribution of Brownian coincidencesMar 15 2019We study the probability distribution, $P_N(T)$, of the coincidence time $T$, i.e. the total local time of all pairwise coincidences of $N$ independent Brownian walkers. We consider in details two geometries: Brownian motions all starting from $0$, and ... More

On the qubit routing problemFeb 21 2019We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing's tket compiler. We present empirical results ... More

Coulomb-gas electrostatics controls large fluctuations of the KPZ equationMar 15 2018Jul 24 2018We establish a large deviation principle for the Kardar-Parisi-Zhang (KPZ) equation, providing precise control over the left tail of the height distribution for narrow wedge initial condition. Our analysis exploits an exact connection between the KPZ ... More

On the qubit routing problemFeb 21 2019Feb 28 2019We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing's tket compiler. We present empirical results ... More

Cold Matter Assembled Atom-by-AtomJul 11 2016The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a novel platform for the deterministic preparation of regular arrays of individually controlled ... More

Superconducting qubitsMay 01 2008From a physicist's standpoint, the most interesting part of quantum computing research may well be the possibility to probe the boundary between the quantum and the classical worlds. The more macroscopic are the structures involved, the better. So far, ... More

Using Monoidal Categories in the Transformational Study of Musical Time-Spans and RhythmsMay 30 2013Aug 06 2013Transformational musical theory has so far mainly focused on the study of groups acting on musical chords, one of the most famous example being the action of the dihedral group D24 on the set of major and minor chords. Comparatively less work has been ... More

Spontaneous symmetry breaking and linear effective potentialsMay 05 2012The convexity of a scalar effective potential is a well known property, and, in the situation of spontaneous symmetry breaking, leads to the so-called Maxwell construction, characterised by a flat effective potential between the minima of the bare potential. ... More

Non critical superstring configuration and Minkowski space time in four dimensionsMar 15 2006Feb 21 2007We extend the non-perturbative time-dependent bosonic string action of [3] to a N=1 supersymmetric world sheet action with graviton background, and assume a superpotential, function of the time super coordinate.

Concepts of Renormalization in PhysicsAug 24 2005A non technical introduction to the concept of renormalization is given, with an emphasis on the energy scale dependence in the description of a physical system. We first describe the idea of scale dependence in the study of a ferromagnetic phase transition, ... More

Space-time percolation and detection by mobile nodesAug 31 2011Sep 09 2015Consider the model where nodes are initially distributed as a Poisson point process with intensity $\lambda$ over $\mathbb{R}^d$ and are moving in continuous time according to independent Brownian motions. We assume that nodes are capable of detecting ... More

A counterexample to the Arakelyan ConjectureJul 01 1992A ``self--similar'' example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.

Multifidelity variance reduction for pick-freeze Sobol index estimationMar 25 2013Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). ... More

Groupes Quantiques d'Interpolation de Langlands de Rang 1Jul 11 2011Interpolating Langlands Quantum Groups of Rank 1 -- We study a certain family, parameterized by an positive integer g, of double deformations of the envelopping algebra U(sl2), in the spirit of arXiv:0809.4453. We prove that each of these double deformations ... More

Dynamical mechanism for ultra-light scalar Dark MatterFeb 11 2015Nov 30 2015Assuming a double-well bare potential for a self-interacting scalar field, with the Higgs vacuum expectation value, it is shown that non-perturbative quantum corrections naturally lead to ultra-light particles of mass $\simeq10^{-23}$eV, if these non-perturbative ... More

A correlation between the amount of dark matter in elliptical galaxies and their shapeJul 28 2014We discuss the correlation between the dark matter content of elliptical galaxies and their ellipticities. We then explore a mechanism for which the correlation would emerge naturally. Such mechanism leads to identifying the dark matter particles to gravitons. ... More

The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice GasesJul 15 2015Jul 19 2015One of the main features of statistical systems out of equilibrium is the currents they exhibit in their stationary state: microscopic currents of probability between configurations, which translate into macroscopic currents of mass, charge, etc. Understanding ... More

Generalized Inversions and the Construction of Musical Group and Groupoid ActionsFeb 06 2014Transformational music theory is a recent field in music theory which studies the possible transformations between musical objects, such as chords. In the framework of the theory initiated by David Lewin, the set of all transformations forms a group which ... More

Non-Hermitian Lagrangian for quasi-relativistic fermionsMay 13 2014Dec 09 2014We present a Lorentz-symmetry violating Lagrangian for free fermions, which is local but not Hermitian, whereas the corresponding Hamiltonian is Hermitian but not local. A specific feature of the model is that the dispersion relation is relativistic in ... More

On inverse scattering at high energies for the multidimensional relativistic Newton equation in a long range electromagnetic fieldDec 31 2013We define scattering data for the relativistic Newton equation in an electric field $-\nabla V\in C^1(\R^n,\R^n)$, $n\ge 2$, and in a magnetic field $B\in C^1(\R^n,A_n(\R))$ that decay at infinity like $r^{-\alpha-1}$ for some $\alpha\in (0,1]$, where ... More

The Lawrence-Krammer representation is a quantization of the symmetric square of the Burau representationSep 21 2016We show that the Lawrence--Krammer representation can be obtained as the quantization of the symmetric square of the Burau representation. This construction allows us to find new representations of the braid groups.

Complexity of inheritance of $\mathcal{F}$-convexity for restricted games induced by minimum partitionsAug 25 2016Let $G = (N,E,w)$ be a weighted communication graph (with weight function $w$ on $E$). For every subset $A \subseteq N$, we delete in the subset $E(A)$ of edges with ends in $A$, all edges of minimum weight in $E(A)$. Then the connected components of ... More

Stacking machine learning classifiers to identify Higgs bosons at the LHCDec 21 2016May 30 2017Machine learning (ML) algorithms have been employed in the problem of classifying signal and background events with high accuracy in particle physics. In this paper, we compare the performance of a widespread ML technique, namely, \emph{stacked generalization}, ... More

Convexity at finite temperature and non-extensive thermodynamicsMar 04 2016Aug 02 2016Assuming that tunnel effect between two degenerate bare minima occurs, in a scalar field theory at finite volume, this article studies the consequences for the effective potential, to all loop orders. Convexity is achieved only if the two bare minima ... More

The index of G-transversally elliptic families in KK-theoryMar 29 2018We define and study the index map for families of G-transversally elliptic operators and introduce the multiplicity for a given irreducible representation as a virtual bundle over the base of the fibration. We then prove the usual axiomatic properties ... More

The index of G-transversally elliptic families in cohomologySep 13 2018We define the Chern character of the index class of a $G$-invariant family of $G$-transversally elliptic operators, see [6]. Next we study the Berline-Vergne formula for families in the elliptic and transversally elliptic case.

The endomorphism ring of projectives and the Bernstein centreMar 05 2018Dec 13 2018Let $F$ be a finite extension of $\mathbb {Q}_{p}$ and $\mathcal{O}_F$ its ring of integers. Let $\Omega$ be a Bernstein component and let $(J, \lambda)$ be an $\Omega$-type. In this paper we will prove that the centre of the Bernstein component $\Omega$ ... More

Inheritance of Convexity for the $\mathcal{P}_{\min}$-Restricted GameAug 08 2017May 17 2018We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This ... More

Regularized maximum of strictly plurisubharmonic functions on an almost complex manifoldMar 21 2013Mar 28 2013We prove that the maximum of two smooth strictly plurisubharmonic functions on an almost complex manifold can be uniformly approximated by smooth strictly plurisubharmonic functions.

On links between horocyclic and geodesic orbits on geometrically infinite surfacesJul 25 2017We study the topological dynamics of the horocycle flow $h_\mathbb{R}$ on a geometrically infinite hyperbolic surface S. Let u be a non-periodic vector for $h_\mathbb{R}$ in T^1 S. Suppose that the half-geodesic $u(\mathbb{R}^+)$ is almost minimizing ... More

Implicative algebras: a new foundation for realizability and forcingFeb 02 2018Mar 15 2018We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this structure is that ... More

Band-structure and electronic transport calculations in cylindrical wires : the issue of bound states in transfer-matrix calculationsJul 16 2019The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the energy spectrum. ... More

On inverse problems for the multidimensional relativistic Newton equation at fixed energyJul 03 2006In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results, we obtain, ... More

The Ismagilov conjecture over a finite field ${\mathbb F}_p$Dec 04 2016Jan 31 2017We construct the so-called quasiregular representations of the group $B_0^{\mathbb N}({\mathbb F}_p)$ of infinite upper triangular matrices with coefficients in a finite field and give the criteria of theirs irreducibility in terms of the initial measure. ... More

A berndtsson-Andersson operator solving \bar\partial-equation with W^α-estimates on convex domains of finite typeFeb 22 2010In this article, we use a Berndtsson-Andersson operator and the Bergman metric in order to solve the $\bar\partial$ equation on convex domains of finite type for forms satisifying a Carleson condition and get norm estimates of the solution in term of ... More

Euler-Poincaré obstruction for pretzels with long tentacles à la Cantor-NyikosDec 22 2011We present an avatar of the Euler obstruction to foliated structures on certain non-metric surfaces. This adumbrates (at least for the simplest 2D-configurations) that the standard mechanism---to the effect that the devil of algebra sometimes barricades ... More

Ebullition in foliated surfaces versus gravitational clumpingNov 24 2011For surfaces, we brush a reasonably sharp picture of the influence of the fundamental group upon the complexity of foliated-dynamics. A metaphor emerges with phase-changes through the solid-liquid-gaseous states. Groups of ranks $0\le r\le 1$ are frozen ... More

On the Limiting Absorption Principle at zero energy for a new class of possibly non self-adjoint Schr{ö}dinger operatorsAug 23 2018Dec 20 2018We recall a Moure theory adapted to non self-adjoint operators and we apply this theory to Schr{\"o}dinger operators with non real potentials, using different type of conjugate operators. We show that some conjugate operators permits to relax conditions ... More

On the acylindrical hyperbolicity of the tame automorphism group of $\mathrm{SL}_2(\mathbb{C})$Dec 23 2015Jun 30 2016We introduce the notion of \"uber-contracting element, a strengthening of the notion of strongly contracting element which yields a particularly tractable criterion to show the acylindrical hyperbolicity, and thus a strong form of non-simplicity, of groups ... More

A probabilistic algorithm to test local algebraic observability in polynomial timeOct 04 2000The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the remaining variables ... More

Invariant Gaussian fields on homogeneous spaces: explicit constructions and mean nodal volumeFeb 08 2016Jan 30 2019We study the properties of smooth Gaussian random fields defined on a homogeneous space, under the assumption that the probability distribution is invariant under the isometry group of the space. We first indicate, building on early results on Yaglom, ... More

Brody curves omitting hyperplanesDec 14 2008Jan 21 2009A Brody curve, a.k.a. normal curve, is a holomorphic map from the complex line to the complex projective space of dimension n, such that the family of its translations is normal. We prove that Brody curves omitting n hyperplanes in general position have ... More

Normal holomorphic curves from parabolic regions to projective spacesOct 05 2007A holomorphic map from the complex line to a complex projective space is called normal (a. k. a. Brody curve) if it is uniformly continuous from the Euclidean metric to the Fubini--Study metric. The paper contains a survey of known results about such ... More

Co-axial monodromyJun 14 2017For Riemannian metrics of constant positive curvature on a punctured sphere with conic singularities at the punctures and co-axial monodromy of the developing map, possible angles at the singularities are completely described. This completes the recent ... More

Wellposedness and regularity for a degenerate parabolic equation arising in a model of chemotaxis with nonlinear sensitivityDec 12 2012Feb 03 2014We study a one-dimensional parabolic PDE with degenerate diffusion and non-Lipschitz nonlinearity involving the derivative. This evolution equation arises when searching radially symmetric solutions of a chemotaxis model of Patlak-Keller-Segel type. We ... More

Herbert Stahl's proof of the BMV conjectureDec 20 2013The paper contains a simplified version of Stahl's proof of a conjecture of Bessis, Moussa and Villani on the trace of matrices A+tB with Hermitean A and B.

A multi-scale study of a class of hybrid predator-prey modelsSep 01 2014We address the question of an averaging principle for a general class of multi-scale hybrid predator-prey models. We consider prey-predator models where the kinetic of the prey population, described by a differential equation, is faster than the kinetic ... More

John Cage's Number Pieces as Stochastic Processes: a Large-Scale AnalysisNov 17 2013The Number Pieces are a corpus of works by composer John Cage, which rely on a particular time-structure used for determining the temporal location of sounds, named the "time-bracket". The time-bracket system is an inherently stochastic process, which ... More

An Introduction to Non-diffusive Transport ModelsAug 08 2015The process of diffusion is the most elementary stochastic transport process. Brownian motion, the representative model of diffusion, played a important role in the advancement of scientific fields such as physics, chemistry, biology and finance. However, ... More

Exponential convergence to the stationary measure for a class of 1D Lagrangian systems with random forcingJan 08 2016Aug 04 2016We prove exponential convergence to the stationary measure for a class of 1d Lagrangian systems with random forcing in the space-periodic setting: $$ \phi_t+\phi_x^2/2=F^{\omega}, x \in S^1 = \mathbb{R}/\mathbb{Z}. $$ This confirms a part of a conjecture ... More

Un effet de moiré sur les espaces symétriques de type non-compactFeb 11 2016We prove that if $X$ is a symmetric space of the noncompact type, just as adding Helgason waves which propagate in all direction yields an elementary spherical function for $X$, a Helgason wave can be produced by adding elementary spherical functions ... More

Clean measurements of the nucleon axial-vector and free-neutron magnetic form factorsJul 10 2013Jul 21 2014We discuss the feasibility of a weak charged current experiment using a low energy electron beam. A first goal is to measure the Q^2 dependence of the axial-vector form factor g_a(Q^2). It can be measured model-independently and as robustly as for electromagnetic ... More

Single-nucleon experimentsOct 09 2009We discuss the Jefferson Lab low momentum transfer data on moments of the nucleon spin structure functions $g_1$ and $g_2$ and on single charged pion electroproduction off polarized proton and polarized neutron. A wealth of data is now available, while ... More

Simple counterterms for asymptotically AdS spacetimes in Lovelock gravityJul 06 2011Nov 29 2011Although gravitational actions diverge in asymptotically AdS spacetimes, boundary counterterms can be added in order to cancel out those divergences; such counterterms are known in general to third order in the Riemann tensor for the Einstein-Hilbert ... More

Towards A Categorical Approach of Transformational Music TheoryApr 14 2012Jan 23 2014Transformational music theory mainly deals with group and group actions on sets, which are usually constituted by chords. For example, neo-Riemannian theory uses the dihedral group D24 to study transformations between major and minor triads, the building ... More

BUSSTEPP 2016 lecture notes: Exact Wilsonian RenormalizationAug 31 2015Aug 29 2016These lecture notes introduce exact Wilsonian renormalisation, and describe its technical approach, from an intuitive implementation to more advanced realisations. The methods and concepts are explained with a scalar theory, and their extension to quantum ... More

Lifshitz-type Quantum Field Theories in Particle PhysicsSep 26 2011Nov 03 2011This introduction to Lifshitz-type field theories reviews some of its aspects in Particle Physics. Attractive features of these models are described with different examples, as the improvement of graphs convergence, the introduction of new renormalizable ... More

An alternative to exact renormalization equationsMay 03 2005May 09 2005An alternative point of view to exact renormalization equations is discussed, where quantum fluctuations of a theory are controlled by the bare mass of a particle. The procedure is based on an exact evolution equation for the effective action, and recovers ... More

Meromorphic traveling wave solutions of the Kuramoto-Sivashinsky equationApr 25 2005We determine all cases when there exists a meromorphic solution of the third order ODE describing traveling waves solutions of the Kuramoto-Sivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions ... More

Manifold approximation of set-valued functionsJan 11 2009A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.

Sensitivity Analysis Using a Fixed Point Interval IterationNov 18 2008Proving the existence of a solution to a system of real equations is a central issue in numerical analysis. In many situations, the system of equations depend on parameters which are not exactly known. It is then natural to aim proving the existence of ... More

Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with ExclusionFeb 01 2017May 31 2017Dynamical phase transitions are crucial features of the fluctuations of statistical systems, corresponding to boundaries between qualitatively different mechanisms of maintaining unlikely values of dynamical observables over long periods of time. They ... More

Long-Baseline Neutrino Oscillation ExperimentsFeb 06 2011Mar 05 2011During the past decade, long-baseline neutrino experiments played a fundamental role in confirming neutrino flavor change and in measuring the neutrino mixing matrix with high precision. This role will be amplified with the next generation of experiments, ... More

Dark Matter freezeout in modified cosmological scenariosMay 08 2019We study the effects of modifying the expansions history of the Universe on Dark Matter freezeout. We derived a modified Boltzmann equation for freeze-out for an arbitrary energy density in the early Universe and provide an analytic approach using some ... More

The Newman phenomenon and Lucas sequenceAug 26 2011Feb 16 2012This article gives an alternative proof of the fact that N_{Q(zeta)/Q}(1-zeta)=p where p is an odd prime number and zeta is a primitive p-th root of unity, and uses it to prove that N_{Q(zeta)/Q}(1+zeta-zeta^2)=L(p) the p-th Lucas number. It shows a relation ... More

A fractional Brownian field indexed by $L^2$ and a varying Hurst parameterDec 20 2013Apr 23 2014Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space $(0,1/2] \times L^2(T,m)$, $(T,m)$ a separable measure space, where the first coordinate corresponds to the Hurst parameter of fractional Brownian ... More

Permutation Orbifolds and ChaosMay 23 2017Nov 28 2017We study out-of-time-ordered correlation functions in permutation orbifolds at large central charge. We show that they do not decay at late times for arbitrary choices of low-dimension operators, indicating that permutation orbifolds are non-chaotic theories. ... More

Inheritance of Convexity for the $\mathcal{P}_{\min}$-Restricted GameAug 08 2017Jun 20 2019We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This ... More

New self-dual codes of length 72May 16 2017In this paper we obtain at least 61 new singly even (Type I) binary [72,36,12] self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes) and at least 13 new doubly even (Type II) binary [72,36,12] self-dual codes by replacing ... More

Unfolding of Finite Concurrent AutomataOct 05 2018We consider recognizable trace rewriting systems with level-regular contexts (RTL). A trace language is level-regular if the set of Foata normal forms of its elements is regular. We prove that the rewriting graph of a RTL is word-automatic. Thus its first-order ... More

The Chirka - Lindelof and Fatou theorems for d-bar subsolutionsAug 10 2018We prove analogs of the Chirka - Lindelof and Fatou theorems for bounded functions with bounded d-bar on a strictly pseudoconvex domain in an almost complex manifold

The QCD running coupling at all scales and the connection between hadron masses and Λ_sMar 20 2018We report on recent experimental and theoretical developments in our understanding of the QCD running coupling \alpha_s in QCD's nonperturbative regime. They allow us to analytically compute the hadron mass spectrum, with \Lambda_s the only input necessary ... More

A little scholium on Hilbert-Rohn via the total reality of $M$-curves: Riemann's flirt with Miss RagsdaleApr 22 2013This note presents an elementary proof of Hilbert's 1891 Ansatz of nesting for $M$-sextics, along the line of Riemann's Nachlass 1857 and a simple Harnack-style argument (1876). Our proof seems to have escaped the attention of Hilbert (and all subsequent ... More

Value distribution and potential theoryApr 22 2003We describe some results of value distribution theory of holomorphic curves and quasiregular maps, which are obtained using potential theory. Among the results discussed are: extensions of Picard's theorems to quasiregular maps between Riemannian manifolds, ... More

Compact bordered Riemannian surfaces as vibrating membranes: an estimate à la Hersch-Yang-Yau-Fraser-SchoenMay 19 2011We try to present an estimate relating the first Dirichlet and Neumann eigenvalues of a compact bordered Riemannian surface.

Some remarks on contact manifolds, Monge-Ampere equations and solution singularitiesMar 07 2014We describe some natural relations connecting contact geometry, classical Monge-Ampere equations and theory of singularities of solutions to nonlinear PDEs. They reveal the hidden meaning of Monge-Ampere equations and sheds new light on some aspects of ... More

Criteria of irreducibility of the Koopman representations for the group ${\rm GL}_0(2\infty,{\mathbb R})$Oct 15 2016Jan 31 2017Our aim is to find the irreducibility criteria for the Koopman representation, when the group acts on some space with a measure (Conjecture 1.5). Some general necessary conditions of the irreducibility of this representation are established. In the particular ... More

On metrics of constant positive curvature with four conic singularities on the sphereMay 07 2019Jul 16 2019We show that for given four points on the sphere and prescribed angles at these points, which are not multiples of $2\pi$, the number of metrics of curvature 1 having conic singularities with these angles at these points is finite.

Tree metrics and their Lipschitz-free spacesApr 21 2009We compute the Lipschitz-free spaces of subsets of the real line and characterize subsets of metric trees by the fact that their Lipschitz-free space is isometric to a subspace of $L_1$.

On the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representationsAug 28 2018Sep 25 2018Attached to any reductive Lie group $G$ is a "Cartan motion group" $G_0$ $-$ a Lie group with the same dimension as $G$, but a simpler group structure. A natural one-to-one correspondence between the irreducible tempered representations of $G$ and the ... More

On the analogy between real reductive groups and Cartan motion groups. III: A proof of the Connes-Kasparov isomorphismFeb 29 2016Mar 05 2019Alain Connes and Nigel Higson pointed out in the 1990s that the Connes-Kasparov "conjecture"' for the K-theory of reduced groupe $C^\ast$-algebras seemed, in the case of reductive Lie groups, to be a cohomological echo of a conjecture of George Mackey ... More

On the Limiting Absorption Principle for Schr{ö}dinger operators on waveguidesFeb 06 2019We prove a Limiting Absorption Principle for Schr{\"o}dinger operators in tubes about infinite curves embedded in the Euclidian space with different types of boundary conditions. The argument is based on the Mourre theory with conjugate operators different ... More

A New Class of Schrödinger Operators without Positive EigenvaluesNov 20 2017Oct 08 2018Following the proof given by Froese and Herbst in [FH82] with another conjugate operator, we show for a class of real potential that possible eigenfunction of the Schr\"odinger operator has to decay sub-exponentially. We also show that, for a certain ... More

Complexes of groups and geometric small cancellation over graphs of groupsJun 28 2013Feb 06 2014We explain and generalise a construction due to Gromov to realise geometric small cancellation groups over graphs of groups as fundamental groups of non-positively curved 2-dimensional complexes of groups. We then give conditions so that the hyperbolicity ... More

Large values of Hecke-Maass L-functions with prescribed argumentNov 29 2016We investigate the existence of large values of L-functions attached to Maass forms on the critical line with prescribed argument. The results obtained rely on the resonance method developed by Soundararajan and furthered by Hough.

A semilinear parabolic-elliptic chemotaxis system with critical mass in any space dimensionOct 16 2012Jul 15 2013We study radial solutions in a ball of $\mathbb{R}^N$ of a semilinear, parabolic-elliptic Patlak-Keller-Segel system with a nonlinear sensitivity involving a critical power. For $N = 2$, the latter reduces to the classical linear model, well-known for ... More

Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie SymmetriesDec 19 2006Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine derivations} that ... More

Non-unitary set-theoretical solutions to the Quantum Yang-Baxter EquationMar 28 2000Aug 24 2000We develop a theory of non-unitary set-theoretical solutions to the Quantum Yang-Baxter equation. Our results generalize those obtained by Etingof, Schedler and the author. We remark that some of our constructions are similar to constructions obtained ... More

Inflaton in R-dependent potentialApr 06 2009Mar 25 2010We consider a non-minimally coupled inflaton, in a higher order curvature background, leading to a potential which evolves with the curvature scalar of the Universe, and which describes two regimes. The first one is a de Sitter phase, where the potential ... More

Non-renormalization for planar Wess-Zumino modelNov 27 2003Using a non-perturbative functional method, where the quantum fluctuations are gradually set up,it is shown that the interaction of a N=1 Wess-Zumino model in 2+1 dimensions does not get renormalized. This result is valid in the framework of the gradient ... More

A control on quantum fluctuations in 2+1 dimensionsJun 04 2003Aug 29 2003A functional method is discussed, where the quantum fluctuations of a theory are controlled by a mass parameter and the evolution of the theory with this parameter is connected to its renormalization. It is found, in the framework of the gradient expansion, ... More

A misleading Wilsonian fixed pointNov 13 2007We exhibit here, for a scalar theory, an apparently non-trivial Wilsonian fixed point, which surprisingly describes a free theory. This modest note is an observation which can be of interest in the framework of functional methods in Quantum Field Theory. ... More

A note on Liouville theoryMar 29 2005May 12 2005An exact differential equation is derived for the evolution of the Liouville effective action with the mass parameter. This derivation is based on properties of the exponential potential and some consequences of the equation are discussed.