Applications of the Dirichlet principle to finite reversible nearest particle systems
type: Item
instance of: scholarly article
title: Applications of the Dirichlet principle to finite reversible nearest particle systems
zbMATH Open document ID: 0589.60081
DOI: 10.1007/BF00363513
author: Thomas M. Liggett
publication date: 1987-01-01T00:00:00Z
review text: The Dirichlet principle provides a variational expression for the survival probability of a supercritical finite reversible nearest particle system. We use this expression to derive improved bounds on this survival probability, and to develop techniques for comparing different systems with the same critical value.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 3947371
zbMATH Keywords: Dirichlet principle
zbMATH Keywords: reversible nearest particle system
zbMATH Keywords: survival probability
zbMATH Keywords: comparing different systems with the same critical value
MaRDI profile type: Publication
cites work: Discontinuity of the percolation density in one dimensional \(1/| x- y| ^ 2\) percolation models
cites work: Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
cites work: The phase transition in the one-dimensional Ising model with \(1/r^2\) interaction energy
cites work: Critical phenomena for Spitzer's reversible nearest particle systems
cites work: Q5727090
cites work: Two critical exponents for finite reversible nearest particle systems
cites work: Q5185817
cites work: Q3799468
cites work: Q3776357
cites work: Q3820417
cites work: On coupling of renewal processes with use of failure rates
cites work: One dimensional \(1/| j-i| ^ s\) percolation models: The existence of a transition for s\(\leq 2\)
cites work: Stochastic time evolution of one dimensional infinite particle systems
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3947371