The lace expansion on a tree with application to networks of self-avoiding walks
type: Item
instance of: scholarly article
title: The lace expansion on a tree with application to networks of self-avoiding walks
zbMATH Open document ID: 1027.60098
DOI: 10.1016/S0196-8858(02)00507-9
author: Remco van der Hofstad
author: Gordon Slade
published in: Advances in Applied Mathematics
publication date: 2003-09-15T00:00:00Z
review text: The paper provides new developments on the so-called lace expansion on a tree [introduced by \textit{D. Brydges} and \textit{T. Spencer}, Commun. Math. Phys. 97, 125-148 (1985; Zbl 0575.60099)] and applies the results so obtained to the analysis of cycle-free networks of mutually-avoiding spread-out self-avoiding walk on \(Z^d\) with \(d\) greater than four. The lace theory is generalized to deal with time variable indexed by a tree and the laces are classified in acyclic, cyclic and reductible laces. It is shown that for cycle-free network in dimension larger than four, the behaviour is Gaussian with sufficiently spread-out models.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B41
Mathematics Subject Classification ID: 82D20
zbMATH DE Number: 1981407
reviewed by: Guy Jumarie
MaRDI profile type: Publication
cites work: Q5560061
cites work: Self-avoiding walk in 5 or more dimensions
cites work: The scaling limit of lattice trees in high dimensions
cites work: A new approach to the long-time behavior of self-avoiding random walks
cites work: THE LACE EXPANSION FOR SELF-AVOIDING WALK IN FIVE OR MORE DIMENSIONS
cites work: The number and size of branched polymers in high dimensions
cites work: Self-avoiding walk in five or more dimensions. I: The critical behaviour
cites work: Q4848553
cites work: A new inductive approach to the lace expansion for self-avoiding walks
cites work: A generalised inductive approach to the lace expansion
cites work: Self-avoiding walks in five or more dimensions: polymer expansion approach
cites work: Q4693177
cites work: The scaling limit of self-avoiding random walk in high dimensions
cites work: Q4938892
cites work: Entanglement complexity of graphs in Z3
description: scientific article; zbMATH DE number 1981407