Fluctuations and their Glauber dynamics in lattice systems
type: Item
instance of: scholarly article
title: Fluctuations and their Glauber dynamics in lattice systems
zbMATH Open document ID: 0951.60057
author: Alexei Daletskii
author: S. Albeverio
author: Yuri Kondratiev
author: Michael Röckner
published in: Journal of Functional Analysis
publication date: 2000-12-18T00:00:00Z
review text: The authors consider a class of unbounded spin systems on the lattice \(Z^d\) and construct the stochastic dynamics in the fluctuation space [cf. \textit{S. Albeverio}, \textit{Y. Kondratiev} and \textit{M. Röckner}, ibid. 144, No. 2, 394-423 (1997; Zbl 0880.60098)]. It is shown that the generator \(H_\mu\) of the dynamics is constructed by the Dirichlet form of the macroscopic Gaussian measure, but including additionally a coefficient operator related to the original Dirichlet generator for the microscopic stochastic dynamics. Via transporting the generator \(H_\mu\) to the macroscopic fluctuation space, it is also shown that the corresponding generator is nothing but the one for the generalized Ornstein-Uhlenbeck process.
reviewed by: Chengxun Wu
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60K40
zbMATH DE Number: 1340148
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: spin systems
zbMATH Keywords: fluctuations
zbMATH Keywords: Ornstein-Uhlenbeck process
MaRDI profile type: Publication
full work available at URL: jfan.1999.3415
OpenAlex ID: W2084831889
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DOI: 10.1006/JFAN.1999.3415
description: scientific article; zbMATH DE number 1340148