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Towards sharp Bohnenblust--Hille constantsApr 26 2016Oct 03 2016We investigate the optimality problem associated with the best constants in a class of Bohnenblust--Hille type inequalities for $m$--linear forms. While germinal estimates indicated an exponential growth, in this work we provide strong evidences to the ... More

Lower bounds for the constants of the Hardy-Littlewood inequalitiesMay 12 2014Aug 23 2014Given an integer $m\geq2$, the Hardy--Littlewood inequality (for real scalars) says that for all $2m\leq p\leq\infty$, there exists a constant $C_{m,p}% ^{\mathbb{R}}\geq1$ such that, for all continuous $m$--linear forms $A:\ell_{p}^{N}\times\cdots\times\ell_{p}^{N}\rightarrow\mathbb{R}$ ... More

Lower bounds for the complex polynomial Hardy--Littlewood inequalityOct 12 2014The Hardy--Littlewood inequality for complex homogeneous polynomials asserts that given positive integers $m\geq2$ and $n\geq1$, if $P$ is a complex homogeneous polynomial of degree $m$ on $\ell_{p}^{n}$ with $2m\leq p\leq\infty$ given by $P(x_{1},\ldots,x_{n})=\sum_{|\alpha|=m}a_{\alpha ... More

On the constants of the Bohnenblust-Hille inequality and Hardy--Littlewood inequalitiesJul 26 2014Aug 06 2014In this paper, among other results, we improve the best known estimates for the constants of the generalized Bohnenblust-Hille inequality. These enhancements are then used to improve the best known constants of the Hardy--Littlewood inequality; this inequality ... More

Maximal f-vectors of Minkowski sums of large numbers of polytopesJan 31 2010It is known that in the Minkowski sum of $r$ polytopes in dimension $d$, with $r<d$, the number of vertices of the sum can potentially be as high as the product of the number of vertices in each summand. However, the number of vertices for sums of more ... More

Temperature-extended Jarzynski relation: Application to the numerical calculation of the surface tensionFeb 02 2007Apr 05 2007We consider a generalization of the Jarzynski relation to the case where the system interacts with a bath for which the temperature is not kept constant but can vary during the transformation. We suggest to use this relation as a replacement to the thermodynamic ... More

On universality in aging ferromagnetsApr 01 2004Jun 17 2004This work is a contribution to the study of universality in out-of-equilibrium lattice models undergoing a second-order phase transition at equilibrium. The experimental protocol that we have chosen is the following: the system is prepared in its high-temperature ... More

Fermi liquid theory for SU(N) Kondo modelMay 25 2009Sep 23 2009We extend the Fermi liquid theory of Nozi\`eres by introducing the next-to-leading order corrections to the Fermi liquid fixed point. For a general SU(N) Kondo impurity away from half-filling, this extension is necessary to compute observables (resistivity, ... More

$ζ$-regularised spectral determinants on metric graphsJun 10 2010Several general results for the spectral determinant of the Schr\"odinger operator on metric graphs are reviewed. Then, a simple derivation for the $\zeta$-regularised spectral determinant is proposed, based on the Roth trace formula. Two types of boundary ... More

Wigner time delay and related concepts -- Application to transport in coherent conductorsJul 01 2015Feb 19 2016The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems; the case of disorder in 1D ... More

Dirac-Born-Infeld and k-inflation: the CMB anisotropies from string theoryOct 12 2009Inflationary models within string theory exhibit unusual scalar field dynamics involving non-minimal kinetic terms and generically referred to as k-inflation. In this situation, the standard slow-roll approach used to determine the behavior of the primordial ... More

Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorderAug 03 2013Feb 23 2014The $q$-state Potts model with a long-range correlated disorder is studied by means of large-scale Monte Carlo simulations for $q=2,4,8$ and 16. Evidence is given of the existence of a Griffiths phase, where the thermodynamic quantities display an algebraic ... More

Controling the number of focal elementsMar 14 2013A basic belief assignment can have up to 2^n focal elements, and combining them with a simple conjunctive operator will need O(2^2n) operations. This article proposes some techniques to limit the size of the focal sets of the bbas to be combined while ... More

Matters of time directionality in gravitation theoryJun 17 2016Sep 06 2016Several issues related to time directionality as they arise from a semi-classical perspective are discussed which are all directly or indirectly relevant to gravitation theory. Important clarifications are achieved regarding in particular the concept ... More

Introduction to Vertex AlgebrasSep 08 2008Nov 11 2008These lecture notes are intended to give a modest impulse to anyone willing to start or pursue a journey into the theory of Vertex Algebras by reading one of Kac's or Lepowsky-Li's books. Therefore, the primary goal is to provide required tools and help ... More

Analytic torsion of Hirzebruch surfacesJan 05 2004Using different forms of the arithmetic Riemann-Roch theorem and the computations of Bott-Chern secondary classes, we compute the analytic torsion and the height of Hirzebruch surfaces.

Bernoulli coding map and almost sure invariance principle for endomorphisms of $\mathbb{P}^k$Dec 04 2007Dec 06 2008Let $f$ be an holomorphic endomorphism of $\mathbb{P}^k$ and $\mu$ be its measure of maximal entropy. We prove an Almost Sure Invariance Principle for the systems $(\mathbb{P}^k,f,\mu)$. Our class $\cal{U}$ of observables includes the H\"older functions ... More

Phase Reduction in the Noise Induced Escape Problem for Systems close to ReversibilityJul 04 2013We consider n-dimensional deterministic flows obtained by perturbing a gradient flow. We assume that the gradient flow admits a stable curve of stationary points, and thus if the perturbation is not too large the perturbed flow also admits an attracting ... More

Complementability and maximality in different contexts: ergodic theory, Brownian and poly-adic filtrationsFeb 11 2018Sep 21 2018The notions of complementability and maximality were introduced in 1974 by Ornstein and Weiss in the context of the automorphisms of a probability space, in 2008 by Brossard and Leuridan in the context of the Brownian filtrations, and in 2017 by Leuridan ... More

On the supremum of products of symmetric stable processesMay 10 2018We study the asymptotics, for small and large values, of the supremum of a product of symmetric stable processes. We show in particular that the persistence exponent remains the same as for only one process, up to some logarithmic terms.

Cavitation induced by explosion in a model of ideal fluidDec 07 1998We discuss the problem of an explosion in the cubic-quintic superfluid model, in relation to some experimental observations. We show numerically that an explosion in such a model might induce a cavitation bubble for large enough energy. This gives a consistent ... More

Fluctuation-dissipation relation for the Ising-Glauber model with arbitrary exchange couplingsDec 04 2002We derive an exact expression of the response function to an infinitesimal magnetic field for the Ising-Glauber model with arbitrary exchange couplings.nThe result is expressed in terms of thermodynamic averages and does not depend on initial conditions ... More

3D viscous incompressible fluid around one thin obstacleDec 18 2011Jun 20 2013In this article, we consider Leray solutions of the Navier-Stokes equations in the exterior of one obstacle in 3D and we study the asymptotic behavior of these solutions when the obstacle shrinks to a curve or to a surface. In particular, we will prove ... More

On last passage times of linear diffusions to curved boundariesApr 25 2012The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following Robbins & Siegmund, ... More

Optimal curves of genus 1,2 and 3Jan 31 2011In this survey, we discuss the problem of the maximum number of points of curves of genus 1,2 and 3 over finite fields

Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbersMay 01 2012Oct 22 2012Some results on the ordered statistics of eigenvalues for one-dimensional random Schr\"odinger Hamiltonians are reviewed. In the case of supersymmetric quantum mechanics with disorder, the existence of low energy delocalized states induces eigenvalue ... More

On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approachJun 01 2007Feb 19 2008We consider a metric graph $\mathcal{G}$ made of two graphs $\mathcal{G}_1$ and $\mathcal{G}_2$ attached at one point. We derive a formula relating the spectral determinant of the Laplace operator $S_\mathcal{G}(\gamma)=\det(\gamma-\Delta)$ in terms of ... More

The exact numerical treatment of inflationary modelsMar 19 2007Oct 07 2015The precision reached by the recent CMB measurements gives new insights into the shape of the primordial power spectra of the cosmological perturbations. In the context of inflationary cosmology, this implies that the CMB data are now sensitive to the ... More

Fermionic currents flowing along extended objectsNov 09 2002This PhD thesis discusses the internal structure of topological defects, and branes in extra-dimensions, carrying fermionic currents. The general framework in which these objects may appear is presented in the first part while the second part is devoted ... More

A note on one of the Markov chain Monte Carlo novice's questionsApr 14 2015We introduce a novel time-homogeneous Markov embedding of a class of time inhomogeneous Markov chains widely used in the context of Monte Carlo sampling algorithms which allows us to answer one of the most basic, yet hard, question about the practical ... More

Schrödinger operators on fractal lattices with random blow-upsJan 18 2002Starting from a finitely ramified self-similar set $X$ we can construct an unbounded set $X_{<\infty>}$ by blowing-up the initial set $X$. We consider random blow-ups and prove elementary properties of the spectrum of the natural Laplace operator on $X_{<\infty>}$ ... More

Explicit computations of Serre's obstruction for genus 3 curves and application to optimal curvesJan 19 2009Feb 19 2009Let k be a field of characteristic different from 2. There can be an obstruction for an indecomposable principally polarized abelian threefold (A,a) over k to be a Jacobian over k. It can be computed in terms of the rationality of the square root of the ... More

Flexible modelling in statistics: past, present and futureSep 22 2014In times where more and more data become available and where the data exhibit rather complex structures (significant departure from symmetry, heavy or light tails), flexible modelling has become an essential task for statisticians as well as researchers ... More

Minimal and maximal elements in Kazhdan-Lusztig double sided cells of $S_n$ and Robinson-Schensted correspondanceApr 04 2003Nov 17 2005In symmetric groups, a two-sided cell is the set of all permutations which are mapped by the Robinson-Schensted correspondence on a pair of tableaux of the same shape. In this article, we show that the set of permutations in a two-sided cell which have ... More

Loss of Resolution for the Time Reversal of Waves in Random Underwater Acoustic ChannelsJan 24 2012In this paper we analyze a time-reversal experiment in a random underwater acoustic channel. In this kind of waveguide with semi-infinite cross section a propagating field can be decomposed over three kinds of modes: the propagating modes, the radiating ... More

Mixing Least-Squares Estimators when the Variance is UnknownNov 02 2007We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some cases the ... More

Estimation of Gaussian graphs by model selectionOct 10 2007Jul 16 2008We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and focus on the disadvantageous case where n is smaller than p. To estimate the ... More

Two Dimensional Incompressible Ideal Flow Around a Thin Obstacle Tending to a CurveApr 17 2008May 07 2008In this work we study the asymptotic behavior of solutions of the incompressible two-dimensional Euler equations in the exterior of a single smooth obstacle when the obstacle becomes very thin tending to a curve. We extend results by Iftimie, Lopes Filho ... More

Leonardo's rule, self-similarity and wind-induced stresses in treesMay 13 2011Nov 15 2011Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the ... More

Optimal Strouhal number for swimming animalsFeb 01 2011To evaluate the swimming performances of aquatic animals, an important dimensionless quantity is the Strouhal number, St = fA/U, with f the tail-beat frequency, A the peak-to-peak tail amplitude, and U the swimming velocity. Experiments with flapping ... More

Effect of connecting wires on the decoherence due to electron-electron interaction in a metallic ringJul 19 2007We consider the weak localization in a ring connected to reservoirs through leads of finite length and submitted to a magnetic field. The effect of decoherence due to electron-electron interaction on the harmonics of AAS oscillations is studied, and more ... More

Scattering theory on graphs (2): the Friedel sum ruleDec 12 2001Mar 01 2002We consider the Friedel sum rule in the context of the scattering theory for the Schr\"odinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples ... More

Stability of giant vortices in quantum liquidsFeb 03 2004We show how giant vortices can be stabilized in strong external potential Bose-Einstein condensates. We illustrate the formation of these vortices thanks to the relaxation Ginzburg-Landau dynamics for two typical potentials in two spatial dimensions. ... More

Wave turbulence and Bose-Einstein condensatesJan 09 2004Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability density of ... More

A Sequent Calculus for Modelling InterferencesJun 22 2007A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal with multisequent ... More

Secant varieties and successive minimaOct 23 2001Given an arithmetic surface and a positive hermitian line bundle over it, we bound the successive minima of the lattice of global sections of this line bundle. Our method combines a result of C.Voisin on secant varieties of projective curves with previous ... More

Computations of Bott-Chern classes on P(E)May 16 2003We compute the Bott-Chern classes of the metric Euler sequence describing the relative tangent bundle of the variety P(E) of hyperplans of a holomorphic hermitian vector bundle (E,h) on a complex manifold. We give applications to the construction of the ... More

Existence d'une courbe de genre 5 sur F_3 avec 13 points rationnelsFeb 12 2003Let N_q(g) the maximal number of points on a genus g curve over F_q. We prove that N_3(5)=13.

Algebraic homotopy classes of rational functionsDec 11 2009Dec 23 2009We compute the set of naive pointed homotopy classes of endomorphisms of the projective line P^1 over the spectrum of a field. Our computation compares well with Fabien Morel's one of the motivic pointed homotopy classes of endomorphisms of P^1: there ... More

Linearly recursive sequences and Dynkin diagramsApr 23 2012Motivated by a construction in the theory of cluster algebras (Fomin and Zelevinsky), one associates to each acyclic directed graph a family of sequences of natural integers, one for each vertex; this construction is called a {\em frieze}; these sequences ... More

Wave Propagation in Underwater Acoustic Waveguides with Rough BoundariesOct 17 2011Nov 16 2013In underwater acoustic waveguides a pressure field can be decomposed over three kinds of modes: the propagating modes, the radiating modes and the evanescent modes. In this paper, we analyze the effects produced by a randomly perturbed free surface and ... More

Bifurcation into spectral gaps for a noncompact semilinear Schrödinger equation with nonconvex potentialJul 04 2012This paper shows that the nonlinear periodic eigenvalue problem $${cases} -\Delta u + V(x) u - f(x,u) = \lambda u, u \in H^1(\IR^N), {cases}$$ has a nontrivial branch of solutions emanating from the upper bound of every spectral gap of $-\Delta + V$. ... More

Asymptotics of action variables near semi-toric singularitiesDec 07 2014Oct 04 2015The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does ... More

Groupes p-divisibles, groupes finis et modules filtrésSep 01 2000Let k be a perfect field of characteristic p>0. When p>2, Fontaine and Laffaille have classified p-divisibles groups and finite flat p-groups over the Witt vectors W(k) in terms of filtered modules. Still assuming p>2, we extend these classifications ... More

Theoretical Basis for a Solution to the Cosmic Coincidence ProblemMar 03 2006May 31 2010Following a short discussion of some unresolved issues in the standard model of cosmology (considered to be a generic $\Lambda$CDM model with flat geometry and an early period of inflation), we describe the current state of research on the problem of ... More

Two Dimensional Incompressible Ideal Flow Around a Small CurveFeb 04 2011We study the asymptotic behavior of solutions of the two dimensional incompressible Euler equations in the exterior of a curve when the curve shrinks to a point. This work links two previous results: [Iftimie, Lopes Filho and Nussenzveig Lopes, Two Dimensional ... More

Two Dimensional Incompressible Viscous Flow Around a Thin Obstacle Tending to a CurveJul 10 2008Feb 13 2009In [Lacave, IHP, ana, to appear (2008)] the author considered the two dimensional Euler equations in the exterior of a thin obstacle shrinking to a curve and determined the limit velocity. In the present work, we consider the same problem in the viscous ... More

A far-from-equilibrium fluctuation-dissipation relation for an Ising-Glauber-like modelMar 26 2003Jul 21 2003We derive an exact expression of the response function to an infinitesimal magnetic field for an Ising-Glauber-like model with arbitrary exchange couplings. The result is expressed in terms of thermodynamic averages and does not depend on the initial ... More

From symmetries of the modular tower of genus zero real stable curves to an Euler class for the dyadic circleJun 07 2000Feb 14 2001We build actions of Thompson group V (related to the Cantor set) and of the so-called "spheromorphism" group of Neretin, on "towers" of moduli spaces of genus zero real stable curves. The latter consist of inductive limits of spaces which are the real ... More

Mazur's inequality and laffaille's theoremSep 02 2015We look at various questions related to filtrations in $p$-adic Hodgetheory, using a blend of building and Tannakian tools. Specifically,Fontaine and Rapoport used a theorem of Laffaille on filtered isocrystalsto establish a converse of Mazur's inequality ... More

Stability of the Griffiths phase in the 2D Potts model with correlated disorderApr 25 2014A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D $q$-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with the lattice ... More

Fermionic massive modes along cosmic stringsJun 15 2001Nov 05 2001The influence on cosmic string dynamics of fermionic massive bound states propagating in the vortex, and getting their mass only from coupling to the string forming Higgs field, is studied. Such massive fermionic currents are numerically found to exist ... More

Euler and magic squares (De quadratis magicis)Jul 19 2006Jul 20 2006Magic squares have always been and are still fascinating for many people, be it only because of their mathematical properties. Their origin is still but certain : we find no magic squares in Greece, and only a 3x3 one in China at the beginning of our ... More

Christoffel words and Markoff triplesSep 19 2008Markoff triples are parametrized uniquely by Christoffel words.

Indentation, elasticity and surface tensionApr 03 2019The classical models of Hertz, Sneddon and Boussinesq provide solutions for problems of indentation of a semi-infinite elastic massif by a sphere, a sphere or a cone and a flat punch. Although these models have been widely tested, it appears that at small ... More

On the Ritt property and weak type maximal inequalities for convolution powers on $\ell^1(\Z)$Jan 21 2016In this paper we study the behaviour of convolution powers of probability measures $\mu$ on $\Z$, such that $(\mu(n))_{n\in \N}$ is completely monotone or such that $\nu$ is centered with a second moment. In particular we exhibit many new examples of ... More

On the dimension of invariant measures of endomorphisms of $\mathbb{CP}^k$Sep 16 2008Apr 13 2010Let $f$ be an endomorphism of $\mathbb{CP}^k$ and $\nu$ be an $f$-invariant measure with positive Lyapunov exponents $(\lambda_1,\...,\lambda_k)$. We prove a lower bound for the pointwise dimension of $\nu$ in terms of the degree of $f$, the exponents ... More

Constructions of minimal periodic surfaces and minimal annuli in Sol3Nov 20 2013We construct two one-parameter families of minimal properly embedded surfaces in the Lie group Sol3 using a Weierstrass-type representation. These surfaces are not invariant by a one-parameter group of ambient isometries. The first one can be viewed as ... More

Infinite energy solutions to the Navier-Stokes equations in the half-space and applicationsMar 06 2018This short note serves as an introduction to the papers arXiv:1711.01651 and arXiv:1711.04486 by Maekawa, Miura and Prange. These two works deal with the existence of mild solutions on the one hand and local energy weak solutions on the other hand to ... More

Wave Propagation in Shallow-Water Acoustic Random WaveguidesNov 30 2009In shallow-water waveguides a propagating field can be decomposed over three kinds of modes: the propagating modes, the radiating modes and the evanescent modes. In this paper we consider the propagation of a wave in a randomly perturbed waveguide and ... More

Local model of semi-toric integrable systems: theory and applicationsAug 06 2014Oct 05 2015In this article we show how one can use the local models of integrable Hamiltonian systems near critical points to prove a localization theorem for certain singular loci of integrables semi-toric systems for dimension greater than 4.

Numerical study of Schramm-Loewner Evolution in the random 3-state Potts modelJun 18 2010We have numerically studied the properties of the interface induced in the ferromagnetic random-bond three-state Potts model by symmetry-breaking boundary conditions. The fractal dimension $d_f$ of the interface was determined. The corresponding SLE parameter ... More

Numerical study of the critical phases of the frustrated Z(5) modelFeb 25 2016Jun 03 2016The phase diagram of the $\mathbb{Z}(5)$ spin model is studied numerically on the square lattice by means of the {\sl Density Matrix Renormalization Group}. In the regime where the two nearest-neighbor couplings have opposite signs, a critical phase, ... More

Wave-induced motion of magnetic spheresJan 06 2016We report an experimental study of the motion of magnetized beads driven by a travelling wave magnetic field. For sufficiently large wave speed, we report the existence of a backward motion, in which the sphere can move in the direction opposite to the ... More

Filtrations and BuildingsNov 20 2014Mar 09 2015We construct and study a scheme theoretical version of the Tits vectorial building, relate it to filtrations on fiber functors, and use them to clarify various constructions pertaining to Bruhat-Tits buildings, for which we also provide a Tannakian description. ... More

DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock modelJul 22 2014Oct 12 2014The two Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional 5-state clock model are studied on infinite strips using the DMRG algorithm. Because of the open boundary conditions, the helicity modulus $\Upsilon_2$ is computed by imposing ... More

Mixing time of A + B -> 0 in 1DAug 18 2014Aug 17 2015A mixing time density of $A + B \to 0$ on a finite one dimensional domain is defined for general initial and boundary conditions in which $A$ and $B$ diffuse at the same rate. The density is a measure of the number of $A$ and $B$ particles that mix through ... More

Beyond two criteria for supersingularity: coefficients of division polynomialsMar 20 2013Let E: y^2 = x^3 + Ax + B be an elliptic curve defined over a finite field of characteristic p\geq 3. In this paper we prove that the coefficient at x^{p(p-1)/2} in the p-th division polynomial \psi_p(x) of E equals the coefficient at x^{p-1} in (x^3 ... More

Tomorrow's Metamaterials: Manipulation of Electromagnetic Waves in Space, Time and SpacetimeFeb 13 2016Metamaterials represent one of the most vibrant fields of modern science and technology. They are generally dispersive structures in the direct and reciprocal space and time domains. Upon this consideration, I overview here a number of metamaterial innovations ... More

Distribution of the resistance of nanowires with strong impuritiesMay 22 2007Motivated by recent experiments on nanowires and carbon nanotubes, we study theoretically the effect of strong, point-like impurities on the linear electrical resistance R of finite length quantum wires. Charge transport is limited by Coulomb blockade ... More

Preliminary BABAR results on B0 mixing with dileptons and on lifetime with partially reconstructed B0 decaysNov 03 2000With an integrated luminosity of 7.7 fb-1 collected on resonance by BABAR at the PEP-II asymmetric B Factory, we measure the difference in mass between the neutral B eigenstates, Delta(m_d), to be (0.507+/-0.015+/-0.022)x 10^{12} hbar s^{-1} with dileptons ... More

Topologically equisingular deformations of homogeneous hypersurfaces with line singularities are equimultipleJun 26 2015We prove that if $\{f_t\}$ is a family of line singularities with constant L\^e numbers and such that $f_0$ is a homogeneous polynomial, then $\{f_t\}$ is equimultiple. This extends to line singularities a well known theorem of A. M. Gabri\`elov and A. ... More

Asymptotic analysis of boundary layer correctors in periodic homogenizationMay 07 2012This paper is devoted to the asymptotic analysis of boundary layers in periodic homogenization. We investigate the behaviour of the boundary layer corrector, defined in the half-space $\Omega_{n,a}:=\{y\cdot n-a>0\}$, far away from the boundary and prove ... More

Some limiting laws associated with the integrated Brownian motionJul 04 2013We study some limit theorems for the normalized law of integrated Brownian motion perturbed by several examples of functionals: the first passage time, the nth passage time, the last passage time up to a finite horizon and the supremum. We show that the ... More

A quasi-potential for conservation laws with boundary conditionsOct 18 2010We compute the quasi-potential and determine minimizing paths for an action functional related to scalar conservation laws on an interval with boundary conditions in the sense of Bardos et al. (1979). Taking as input an exclusion-like flux function, a ... More

Effects of high vs moderate-intensity training on neuroplasticity and functional recovery after focal ischemiaFeb 08 2018Background and Purpose: This study was designed to compare the effects of high-intensity interval training (HIT) and moderate-intensity continuous training (MOD) on functional recovery and cerebral plasticity during the first 2 weeks following cerebral ... More

Non Gaussian extrema counts for CMB mapsJul 10 2011In the context of the geometrical analysis of weakly non Gaussian CMB maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic ... More

The invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3DJul 09 2009Mar 30 2010The full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian is presented in 2 and 3D. It allows for explicit expression for the Euler characteristic in ND and computation of ... More

Limit Theorems for the Left Random Walk on GLd (R)Mar 07 2016Motivated by a recent work of Benoist and Quint and extending results from the PhD thesis of the third author, we obtain limit theorems for products of independent and identically distributed elements of GLd (R), such as the Marcinkiewicz-Zygmund strong ... More

Complete determination of the zeta function of the Hilbert scheme of $n$ points on a two-dimensional torusOct 25 2016We compute the coefficients of the polynomials $C_n(q)$ defined by the equation \begin{equation*} 1 + \sum_{n\geq 1} \, \frac{C_n(q)}{q^n} \, t^n = \prod_{i\geq 1}\, \frac{(1-t^i)^2}{1-(q+q^{-1})t^i + t^{2i}} \, . \end{equation*} As an application we ... More

Regularities and symmetries in atomic structure and spectraMay 23 2013The use of statistical methods for the description of complex quantum systems was primarily motivated by the failure of a line-by-line interpretation of atomic spectra. Such methods reveal regularities and trends in the distributions of levels and lines. ... More

Random-matrix theory and complex atomic spectraAug 20 2012Around 1950, Wigner introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of random-matrix theory has grown tremendously, with applications ... More

Théorème de Kaplansky effectif pour des valuations de rang 1 centrées sur des anneaux locaux réguliers et completsMar 19 2012Mar 25 2013We prove that any complete regular local ring with a valuation of rank 1 can be embedded, as a valued ring, in a ring of generalized Puiseux expansions.

On the symmetry of the partition function of some square ice modelsMar 04 2009We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set to the special ... More

Keys and alternating sign matricesNov 14 2007May 18 2009Lascoux and Sch\"utzenberger introduced a notion of key associated to any Young tableau. More recently Lascoux defined the key of an alternating sign matrix by recursively removing all -1's in such matrices. But alternating sign matrices are in bijection ... More

Commutation relations of operator monomialsNov 20 2012In this short paper, the commutator of monomials of operators obeying constant commutation relations is expressed in terms of anticommutators. The formula involves Bernoulli numbers or Euler polynomials evaluated in zero. The role of Bernoulli numbers ... More

Koopmans' theorem in statistical Hartree-Fock theoryJun 06 2011In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing ... More

Kinematics of the most efficient ciliumApr 27 2012In a variety of biological processes, eukaryotic cells use cilia to transport flow. Although cilia have a remarkably conserved internal molecular structure, experimental observations report very diverse kinematics. To address this diversity, we determine ... More

Localization for one-dimensional random potentials with large local fluctuationsJul 04 2008Oct 27 2008We study the localization of wave functions for one-dimensional Schr\"odinger Hamiltonians with random potentials $V(x)$ with short range correlations and large local fluctuations such that $\int\D{x} \smean{V(x)V(0)}=\infty$. A random supersymmetric ... More

Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality classMay 14 2004Mar 20 2006The probability P(alpha, N) that search algorithms for random Satisfiability problems successfully find a solution is studied as a function of the ratio alpha of constraints per variable and the number N of variables. P is shown to be finite if alpha ... More