相关论文: Weighted $L^2$-contractivity of Langevin dynamics …
Langevin dynamics is used to study equilibrium properties of the suspension of magnetic filaments (chains of nanoparticles permanently crosslinked with polymers). It is shown that the filament suspension generally has a larger magnetic…
Following the breakthrough work of Guillen and Silvestre \cite{GS24}, that shows that the Fisher information is monotonically decreasing for solutions to the homogeneous Landau equation, we study, for the same equation, the monotonicity…
In this paper, we quantitative convergence in $W_2$ for a family of Langevin-like stochastic processes that includes stochastic gradient descent and related gradient-based algorithms. Under certain regularity assumptions, we show that the…
In this article we develop a new abstract strategy for proving ergodicity with explicit computable rate of convergence for diffusions associated with a degenerate Kolmogorov operator L. A crucial point is that the evolution operator L may…
For a dynamical system, it is known that the existence of a Lyapunov-type density function, called Lyapunov density or Rantzer's density function, implies convergence of Lebesgue almost all solutions to an equilibrium. Using the duality…
This paper is concerned with a class of multivariable stochastic Hamiltonian systems whose generalised position is related by an ordinary differential equation to the momentum governed by an Ito stochastic differential equation. The latter…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
We offer a measure-theoretic extension of the concept and theory of $k$-contraction, including their generalization on fractional dimensions $d$. The respective contraction property is defined through the exponential decay of the…
We consider the Lee-Wick (LW) finite electrodynamics, i.e., the U(1) gauge theory where a (gauge-invariant) dimension-6 operator containing higher-derivatives is added to the free Lagrangian of the U(1) sector. Three bounds on the LW heavy…
We prove $L^{2}$ estimates and solvability for a variety of simply characteristic constant coefficient partial differential equations $P(D)u=f$. These estimates \[||u||_{L^2(D_{r})}\le C\sqrt{d_{r}d_{s}} ||f||_{_{L^2(D_{s})}}\] depend on…
We consider a system of interacting particles governed by the generalized Langevin equation (GLE) in the presence of external confining potentials, singular repulsive forces, as well as memory kernels. Using a Mori-Zwanzig approach, we…
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
We investigate the large-time behavior of the pressureless Euler system with nonlocal velocity alignment and interaction forces, with the aim of characterizing the asymptotic convergence of classical solutions under general interaction…
Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin…
We study long time behavior of some nonlinear discrete velocity kinetic equations in the one and three dimensions with periodic boundary conditions. We prove the exponential time decay of solutions towards the global equilibrium in the…
Both linear and nonlinear Langevin equations are derived directly from the Liouville equation for an exactly solvable model consisting of a Brownian particle of mass $M$ interacting with ideal gas molecules of mass $m$ via a quadratic…
This work deals with the large time behaviour of the spatially homogeneous Landau equation with Coulomb potential. Firstly, we obtain a bound from below of the entropy dissipation $D(f)$ by a weighted relative Fisher information of $f$ with…
In this work we consider the unbiased estimation of expectations w.r.t.~probability measures that have non-negative Lebesgue density, and which are known point-wise up-to a normalizing constant. We focus upon developing an unbiased method…
In his work about hypocercivity, Villani [18] considers in particular convergence to equilibrium for the kinetic Langevin process. While his convergence results in L 2 are given in a quite general setting, convergence in entropy requires…
The long-time/large-scale, small-friction asymptotic for the one dimensional Langevin equation with a periodic potential is studied in this paper. It is shown that the Freidlin-Wentzell and central limit theorem (homogenization) limits…