The lace expansion and its applications: Ecole d’Ete de Probabilites de Saint-Flour XXXIV, 2004

Gordon Slade, Jean Picard3540311890, 9783540311898, 9783540355182

The lace expansion is a powerful and flexible method for understanding the critical scaling of several models of interest in probability, statistical mechanics, and combinatorics, above their upper critical dimensions. These models include the self-avoiding walk, lattice trees and lattice animals, percolation, oriented percolation, and the contact process. This volume provides a unified and extensive overview of the lace expansion and its applications to these models. Results include proofs of existence of critical exponents and construction of scaling limits. Often, the scaling limit is described in terms of super-Brownian motion.

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Table of contents :
1879-front-matter……Page 1
1879-1-6……Page 11
1879-7-17……Page 17
1879-19-29……Page 28
1879-31-40……Page 39
1879-41-55……Page 49
1879-57-65……Page 64
1879-67-75……Page 73
1879-77-86……Page 82
1879-87-108……Page 92
1879-109-123……Page 114
1879-125-139……Page 129
1879-141-149……Page 144
1879-151-159……Page 153
1879-161-170……Page 162
1879-171-182……Page 172
1879-183-200……Page 184
1879-201-210……Page 202
1879-back-matter……Page 212