Kawasaki dynamics in the continuum via generating functionals evolution
type: Item
instance of: scholarly article
zbMATH Open document ID: 1249.82007
author: D. L. Finkelshtein
author: Yuri Kondratiev
author: M. J. Oliveira
publication date: 2012-07-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1107.4450
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 46G20
Mathematics Subject Classification ID: 46E50
zbMATH DE Number: 6056408
zbMATH Keywords: Kawasaki dynamics
zbMATH Keywords: generating functionals
zbMATH Keywords: Vlasov-type scaling
MaRDI profile type: Publication
arXiv ID: 1107.4450
arXiv classification: math-ph
arXiv classification: math.MP
title: Kawasaki dynamics in the continuum via generating functionals evolution
published in: Methods of Functional Analysis and Topology
review text: The Kawasaki dynamics is an example of a hopping particle model, where particles hop randomly over the space \(\mathbb R^d\) according to a rate depending on the interaction between particles (see, for example, [\textit{Y. Kondratiev, E. Lytvynov} and \textit{M. Röckner}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10, No. 2, 185--209 (2007; Zbl 1142.60064)]).NEWLINENEWLINE The authors construct the time evolution of Kawasaki dynamics for a spatial infinite particle systems in terms of generating functionals. This is carried out via the approach of Ovsjannikov type (using a scale of Banach spaces) leading to a solution local in time. An application to Vlasov-type scaling in terms of generating functionals is given.
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 6056408