The Lace Expansion and its Applications

Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004

  • Gordon Slade
  • Jean Picard

Part of the Lecture Notes in Mathematics book series (LNM, volume 1879)

About this book

Introduction

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.

Keywords

Brownian excursion Brownian motion Combinatorics Lattice Power branching random walk contact process lace expansion lattice trees mechanics percolation proof random walk self-avoiding walk super-Brownian motion

Authors and affiliations

  • Gordon Slade
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

Editors and affiliations

  • Jean Picard
    • 1
  1. 1.Laboratoire de Mathématiques Appliquées UMR CNRS 6620Université Blaise Pascal Clermont-FerrandAubière CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/b128444
  • Copyright Information Springer 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-31189-8
  • Online ISBN 978-3-540-35518-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book