TY - JOUR
T1 - High-dimensional graphical networks of self-avoiding walks
AU - Holmes, M
AU - Jarai, Antal A.
AU - Sakai, A
AU - Slade, G
PY - 2004/2
Y1 - 2004/2
N2 - We use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are permitted to take large steps. We study the asymptotic behaviour of networks in the limit of widely separated network branch points, and prove Gaussian behaviour for sufficiently spread-out networks on Zd in dimensions d>4.
AB - We use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are permitted to take large steps. We study the asymptotic behaviour of networks in the limit of widely separated network branch points, and prove Gaussian behaviour for sufficiently spread-out networks on Zd in dimensions d>4.
UR - http://math.ca/10.4153/CJM-2004-005-1
UR - https://www.scopus.com/pages/publications/1342267525
M3 - Article
VL - 56
SP - 77
EP - 114
JO - Canadian Journal of Mathematics - Journal Canadien de Mathematiques
JF - Canadian Journal of Mathematics - Journal Canadien de Mathematiques
ER -