Traces of semigroups associated with interacting particle systems
type: Item
instance of: scholarly article
title: Traces of semigroups associated with interacting particle systems
zbMATH Open document ID: 1147.58016
author: Alexander Kalyuzhnyi
author: S. Albeverio
author: Alexei Daletskii
published in: Journal of Functional Analysis
publication date: 2007-06-26T00:00:00Z
review text: The authors start from a complete connected, oriented manifold of infinite volume with a lower bounded curvature. They also assume that an infinite discrete group of isometries on \(X\) is given such that \(X/G\) is a compact Riemannian manifold. The set \( \Gamma _{X}\) of all locally finite subsets of \(X\) is called the configuration space of \(X\) and is assumed to be equipped with a Gibbs measure which is invariant under the natural action of \(G\) on the configuration space and satisfies a condition known under the name of a ``Ruelle bound''. Finally, they consider a special random measure on \(X\). In this context, they then study the Witten Laplacian on \(X\). In particular, they prove the finiteness of the associated \(\theta\)-function, and its von Neumann realization, and the existence of the corresponding \(L ^{2}\)-Betti numbers.
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 5167471
zbMATH Keywords: Witten Laplacian
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: Betti numbers
zbMATH Keywords: configuration space
reviewed by: Otto Liess
MaRDI profile type: Publication
full work available at URL: j.jfa.2007.01.016
OpenAlex ID: W2089619101
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DOI: 10.1016/J.JFA.2007.01.016
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description: scientific article; zbMATH DE number 5167471