The lace expansion and its applications
著者
書誌事項
The lace expansion and its applications
（Lecture notes in mathematics, 1879 . Ecole d'eté de probabilités de Saint-Flour / editor,
Springer, c2006
- タイトル別名
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The lace expansion and its applications, St. Flour 2004
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注記
"Three series of lectures were given at the 34th Probability Summer School in Saint-Flour (July 6-24, 2004)"--Foreword
Includes in bibliographical references (p. [211]-220) and index
"ISSN Ecole d'été de probabilités de St-Flour, print edition: 0721-5363"--T.p. verso
内容説明・目次
内容説明
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.
目次
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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