相关论文: On The Cutoff Phenomenon For Dyson-Laguerre Proces…

We develop a rigorous framework for quantifying quantum coherence in finite-dimensional systems by applying the Schur-Horn majorization theorem to relate eigenvalue distributions and diagonal entries of density matrices. Building on this…

We estimate the rate of convergence for the Kantorovich (or Wasserstein) distance between empirical measures of i.i.d. random variables associated with the Laguerre model of order $\alpha$ on $(0,\infty)^N$ and their common law, which is…

The exponential contraction in $L^1$-Wasserstein distance and exponential convergence in $L^q$-Wasserstein distance ($q\geq 1$) are considered for stochastic differential equations with irregular drift. When the irregular drift drift is…

We study the cut-off phenomenon for a family of stochastic small perturbations of a one dimensional dynamical system. We will focus in a semi-flow of a deterministic differential equation which is perturbed by adding to the dynamics a white…

We provide an estimation of the dissipation of the Wasserstein 2 distance between the law of some interacting $N$-particle system, and the $N$ times tensorized product of solution to the corresponding limit nonlinear conservation law. It…

This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding…

We propose a solution to the puzzle of dimensional reduction in the random field Ising model, inverting the question and asking: to what random problem in $D=d+2$ dimensions does a pure system in $d$ dimensions correspond? We consider two…

Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's…

We present a new lower bound on the differential entropy rate of stationary processes whose sequences of probability density functions fulfill certain regularity conditions. This bound is obtained by showing that the gap between the…

Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, and let $U$ be a subset of $X$ whose complement is compact. We use the exponential mixing results for diagonalizable flows on $X$ to give upper estimates for the…

This paper is dedicated to providing new tools and methods for studying the trend to equilibrium of gradient flows in metric spaces in the entropy and metric sense, to establish decay rates, finite time of extinction, and to characterize…

Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…

The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…

In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…

We derive two estimates for the deviation of the $N$-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our…

We develop a unifying theory for four different objects: (1) infinite systems of interacting massive particles; (2) solutions to the Dean-Kawasaki equation with singular drift and space-time white noise; (3) Wasserstein diffusions with a.s.…

A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this…

Building on our recent derivation of the Ward-Schwinger-Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we made sure that they had the…

We consider the contact process on a countable-infinite and connected graph of bounded degree. For this process started from the upper invariant measure, we prove certain uniform mixing properties under the assumption that the infection…

We establish the existence of solutions to common noise McKean-Vlasov martingale problems for coefficients with low regularity. Our approach is able to handle the key challenge posed by drift coefficients that are discontinuous with respect…