Improved upper bounds for the contact process critical value
type: Item
instance of: scholarly article
title: Improved upper bounds for the contact process critical value
zbMATH Open document ID: 0832.60093
author: Thomas M. Liggett
published in: The Annals of Probability
publication date: 1996-02-20T00:00:00Z
review text: The basic one-dimensional contact process is a typical interacting particle system. It exhibits the phase transitions with critical value \(\lambda_c\). The precise value \(\lambda_c\) remains unknown up to now. The best known bounds are \(1.539 < \lambda_c < 2\). The upper bound is due to \textit{R. Holley} and the author [Ann. Probab. 6, 198-206 (1978; Zbl 0375.60111)]. The original proof is based on a renewal measure. The author develops a new technique. That is, using some perturbations of the measure instead of the original one. This needs a careful design and a lot of computations. In any case, the author is able to produce a new upper bound 1.942 by hand computation.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 796516
zbMATH Keywords: contact process
zbMATH Keywords: phase transitions
zbMATH Keywords: critical value
zbMATH Keywords: upper bound
reviewed by: Mu-Fa Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988285
OpenAlex ID: W1967660698
DOI: 10.1214/AOP/1176988285
description: scientific article; zbMATH DE number 796516