Branching processes with lattice spatial dynamics and a finite set of particle generation centers
type: Item
instance of: scholarly article
title: Branching processes with lattice spatial dynamics and a finite set of particle generation centers
zbMATH Open document ID: 1270.60092
DOI: 10.1134/S1064562412040278
published in: Doklady Mathematics
publication date: 2013-01-14T00:00:00Z
review text: The authors consider the simplest model of a branching random walk on \(\mathbb{Z}^d\) with continuous time, one type of particles and without extinction in which the reproduction of only one descendant is possible. If the rate of branching is determined by a nonnegative function \(\beta V(x)\), \(x\in \mathbb{Z}^d\), a correspondence between such branching random walks and the theory of phase transition for homopolymers is established [\textit{M. Cranston} et al., J. Funct. Anal. 256, No. 8, 2656--2696 (2009; Zbl 1162.82031)]. Some results that are similar to the results obtained in [loc cit.], but with substantially different proofs, are presented.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 82D60
Mathematics Subject Classification ID: 82C26
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 6124971
zbMATH Keywords: branching random walk
zbMATH Keywords: potential
zbMATH Keywords: phase transition
zbMATH Keywords: homopolymer
author: S. Molchanov
author: E. B. Yarovaya
reviewed by: Nasir N. Ganikhodjaev
MaRDI profile type: Publication
cites work: Criteria of exponential growth for the numbers of particles in models of branching random walks
cites work: Spectral properties of evolutionary operators in branching random walk models
cites work: Parabolic problems for the Anderson model. I: Intermittency and related topics
cites work: Geometric characterization of intermittency in the parabolic Anderson model
cites work: Continuous model for homopolymers
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description: scientific article; zbMATH DE number 6124971