Related papers: Existence of equilibrium for Infinite System of In…

We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…

We present general existence and uniqueness results for marked models with pair interactions, exemplified through Gibbs point processes on path space. More precisely, we study a class of infinite-dimensional diffusions under Gibbsian…

This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…

We introduce a lattice Boltzmann for simulating an immiscible binary fluid mixture. Our collision rules are derived from a macroscopic thermodynamic description of the fluid in a way motivated by the Cahn-Hilliard approach to…

We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…

We solve the Fokker-Planck equation for Brownian motion in a logarithmic potential. When the diffusion constant is below a critical value the solution approaches a non-normalizable scaling state, reminiscent of an infinite invariant…

We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…

We discuss the interrelation between phase transitions in interacting lattice or continuum models, and the existence of infinite clusters in suitable random-graph models. In particular, we describe a random-geometric approach to the phase…

We study the variational solution of generic interacting fermionic lattice systems using fermionic Gaussian states and show that the process of "gaussification", leading to a nonlinear closed equation of motion for the covariance matrix, is…

We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…

The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is reinvestigated within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we…

We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…

We present a numerical study of the dynamics of a non-ideal fluid subject to a density-dependent pseudo-potential characterized by a hierarchy of nested attractive and repulsive interactions. It is shown that above a critical threshold of…

Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…

The aim of this paper is to study the recovery of a spatially dependent potential in a (sub)diffusion equation from overposed final time data. We construct a monotone operator one of whose fixed points is the unknown potential. The…

We present a new method to describe the kinetics of driven lattice gases with particle-particle interactions beyond hard-core exclusions. The method is based on the time-dependent density functional theory for lattice systems and allows one…

Derrida et al. and Sch\"{u}tz and Stinchcombe gave algebraic formulas for the correlation functions of the partially asymmetric simple exclusion process. Here we give a fairly general recipe of how to get these formulas and extend them to…

We prove uniqueness of a martingale problem with boundary conditions on a simplex associated to a differential operator with an unbounded drift. We show that the solution of the martingale problem remains absorbed at the boundary once it…

The Wigner function of a dynamical infinite dimensional lattice is studied. A closed differential equation without diffusion terms for this function is obtained and solved. We map atom-photon interaction systems, such as the Jaynes-Cummings…

We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…