An infinite system of Brownian balls with infinite range interaction.
type: Item
instance of: scholarly article
title: An infinite system of Brownian balls with infinite range interaction.
zbMATH Open document ID: 1046.60055
DOI: 10.1016/S0304-4149(00)00036-3
author: Myriam Fradon
author: H. Tanemura
author: Sylvie Rœlly
published in: Stochastic Processes and their Applications
publication date: 2004-09-22T00:00:00Z
review text: The authors consider a system of infinitely many indistinguishable hard balls in a \(d\)-dimensional Euclidean space \(\mathbb R^d, d\geq 2\), undergoing Brownian motions and submitted to the influence of a smooth infinite range pair potential \(\Phi _s\). The spatial mean density of the initial configuration is allowed to be arbitrarily large and the balls may interact even if the distance between them is large. The system is represented as a unique strong solution to the infinite-dimensional Skorokhod-type system of equations \[ X_i(t)=X_i+ B_i(t)-\frac {1}{2}\sum _{j\in N}\int _0^t\nabla \Phi _s(X_i(s)-X_j(s))\,ds +\sum _{j\in N}\int _0^t(X_i(s)-X_j(s))\,dL_{ij}(s), \] where \(\{L_{ij}\}\) are the respective local times. Also, some geometrical aspect of the configuration space is discussed and the dynamics of finitely many hard balls is solved. The reversible solution of the equation is shown to be the limit of finite-dimensional approximations.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 2102340
zbMATH Keywords: Gibbs state
zbMATH Keywords: interacting particle system
zbMATH Keywords: percolation model
MaRDI profile type: Publication
cites work: Infinite-dimensional diffusion processes with singular interaction
cites work: Gradient dynamics of infinite point systems
cites work: Gibbs measures and phase transitions
cites work: Unendlich-dimensionale Wienerprozesse mit Wechselwirkung
cites work: Stochastic differential equations with reflecting boundary conditions
cites work: Dirichlet form approach to infinite-dimensional Wiener processes with singular interactions
cites work: Some remarks on the ground state of infinite systems in statistical mechanics
cites work: Stochastic differential equations for multi-dimensional domain with reflecting boundary
cites work: Stochastic differential equations for mutually reflecting Brownian balls
cites work: Q5607484
cites work: Stochastic differential equations with reflecting boundary condition in convex regions
cites work: A system of infinitely many mutually reflecting Brownian balls in \(\mathbb{R}^ d\)
cites work: Uniqueness of Dirichlet forms associated with systems of infinitely many Brownian balls in \({\mathbb R}^ d\)
cites work: Construction of infinite dimensional interacting diffusion processes through Dirichlet forms
description: scientific article; zbMATH DE number 2102340