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

• Main Author: Slade, Gordon (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Picard, Jean (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes in Mathematics, 1879
• Subjects: Mathematics.; Probabilities.; Combinatorics.; Physics.; Probability Theory and Stochastic Processes.; Theoretical, Mathematical and Computational Physics.

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, p...

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.