Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit

Let Γ denote the space of all locally finite subsets (configurations) in \documentclass[12pt]{minimal}\begin{document}$\mathbb {R}^d$\end{document} R d . A stochastic dynamics of binary jumps in continuum is a Markov process on Γ in which pairs of particles simultaneously hop over \documentclass[12p...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 2011-11, Vol.52 (11), p.113301-113301-27
Main Authors: Finkelshtein, Dmitri, Kondratiev, Yuri, Kutoviy, Oleksandr, Lytvynov, Eugene
Format: Article
Language:English
Subjects:
Correlation analysis
Exact sciences and technology
Markov analysis
Mathematical functions
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
Stochastic models
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let Γ denote the space of all locally finite subsets (configurations) in \documentclass[12pt]{minimal}\begin{document}$\mathbb {R}^d$\end{document} R d . A stochastic dynamics of binary jumps in continuum is a Markov process on Γ in which pairs of particles simultaneously hop over \documentclass[12pt]{minimal}\begin{document}$\mathbb {R}^d$\end{document} R d . We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann nonlinear equation for the particle density.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3657345