The Lace Expansion and its Applications
The Lace Expansion and its Applications
Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004
Publié par:Picard, Jean
Contenu
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.
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.
Informations bibliographiques
mai 2006, 233 pages, Lecture Notes in Mathematics, École d'Été de Probabilités de Saint-Flour, Anglais
Springer Nature EN
978-3-540-31189-8