The Lace Expansion and its Applications: Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / Edition 1

The Lace Expansion and its Applications: Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / Edition 1

by Jean Picard, Gordon Slade
     
 

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

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Overview

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.

Product Details

ISBN-13:
9783540311898
Publisher:
Springer Berlin Heidelberg
Publication date:
06/15/2006
Series:
Lecture Notes in Mathematics / Ecole d'Ete de Probabilites de Saint-Flour Series, #1879
Edition description:
2006
Pages:
233
Product dimensions:
6.10(w) x 9.30(h) x 0.60(d)

Table of Contents

Simple Random Walk.- The Self-Avoiding Walk.- The Lace Expansion for the Self-Avoiding Walk.- Diagrammatic Estimates for the Self-Avoiding Walk.- Convergence for the Self-Avoiding Walk.- Further Results for the Self-Avoiding Walk.- Lattice Trees.- The Lace Expansion for Lattice Trees.- Percolation.- The Expansion for Percolation.- Results for Percolation.- Oriented Percolation.- Expansions for Oriented Percolation.- The Contact Process.- Branching Random Walk.- Integrated Super-Brownian Excursion.- Super-Brownian Motion.

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