Related papers: Conservative interacting particles system with ano…

We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent…

In this paper, we consider a family of interacting particle systems on $[-N,N]$ that arises as a natural model for current reservoirs and Fick's law. We study the exponential rate of convergence to the stationary measure, which we prove to…

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…

We consider a class of "most non ergodic" particle systems and prove that for most of them ergodicity appears if only one particle of N has contact with external world, that is this particle collides with external particles in random time…

Systems of particles interacting via inverse-power law potentials have an invariance with respect to changes in length and temperature, implying a correspondence in the dynamics and thermodynamics between different `isomorphic' sets of…

We consider an isomorphism invariant for measure-preserving systems - types of generalized entropy convergence rates. We show the connections of this invariant with the types of Shannon entropy convergence rates. In the case when they…

We consider MCMC algorithms for certain particle systems which include both attractive and repulsive forces, making their convergence analysis challenging. We prove that a version of these algorithms on a bounded state space is uniformly…

We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review…

We analyse certain degenerate infinite dimensional sub-elliptic generators, and obtain estimates on the long-time behaviour of the corresponding Markov semigroups that describe a certain model of heat conduction. In particular, we establish…

We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…

The goal of this paper is to give a short review of recent results of the authors concerning classical Hamiltonian many particle systems. We hope that these results support the new possible formulation of Boltzmann's ergodicity hypothesis…

We prove the convergence at an exponential rate towards the invariant probability measure for a class of solutions of stochastic differential equations with finite delay. This is done, in this non-Markovian setting, using the cluster…

The main aim of this work is to establish an averaging principle for a wide class of interacting particle systems in the continuum. This principle is an important step in the analysis of Markov evolutions and is usually applied for the…

In this paper, we consider a system of heterogeneously interacting quantum particles subject to indirect continuous measurement. The interaction is assumed to be of the mean-field type. We derive a new limiting quantum graphon system, prove…

The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…

A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution…

We consider controllability for divergence-free systems that have a conserved quantity and satisfy a H\"ormander condition. It is shown that such systems are controllable, provided that the conserved quantity is a proper function. The proof…

We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by…

We develop and implement new probabilistic strategy for proving exponential ergodicity for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process in infinite…

We investigate a solvable model for energy conserving non-equilibrium steady states. The time-reversal asymmetry of the dynamics leads to the violation of detailed balance and to ergodicity breaking, as manifested by the presence of…