Related papers: The mean-field Zero-Range process with unbounded m…
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 analyze the equilibrium properties of a chain of ferromagnetically coupled rotators which interact through a force that decays as $r^{-\alpha}$ where r is the interparticle distance and $\alpha\ge 0$. Our model contains as particular…
We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild assumptions on the regularity of the interacting kernels we…
Using the mode-by-mode summation technique the zero point energy of the electromagnetic field is calculated for the boundary conditions given on the surface of an infinite solid cylinder. It is assumed that the dielectric and magnetic…
We study the mixing properties of a Brownian motion whose movements are hindered by semipermeable barriers. Our setting assumes that the process takes values in a smooth planar domain and that the barriers are one-dimensional closed curves.…
We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…
We study a harmonically confined Bose-Bose mixture using quantum Monte Carlo methods. Our results for the density profiles are systematically compared with mean-field predictions derived through the Gross-Pitaevskii equation in the same…
The random-cluster model is a unifying framework for studying random graphs, spin systems and electrical networks that plays a fundamental role in designing efficient Markov Chain Monte Carlo (MCMC) sampling algorithms for the classical…
We present a general method to derive the metastable behavior of weakly mixing Markov chains. This approach is based on properties of the resolvent equations and can be applied to metastable dynamics which do not satisfy the mixing…
Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position of its center of mass $u$, and the statistics of the forces $F(u)$. There are two proposals to…
We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions…
The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…
In this article we show, in a concise manner, a result of uniform in time propagation of chaos for non exchangeable systems of particles interacting according to a random graph. Provided the interaction is Lipschitz continuous, the…
Zero-range processes with decreasing jump rates exhibit a condensation transition, where a positive fraction of all particles condenses on a single lattice site when the total density exceeds a critical value. We study the onset of…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
In coupled rotor models which describe identical rotating nuclei the nuclear spin states restrict the possible angular momenta of each molecule. There are two mean-field approaches to determining the orientational phase diagrams in such…
We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…
The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of…
This paper considers the family of invariant measures of Markovian mean-field interacting particle systems on a countably infinite state space and studies its large deviation asymptotics. The Freidlin-Wentzell quasipotential is the usual…
The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numerical implementation of the method. First, we describe how the…