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＜E-Book＞
The Lace Expansion and its Applications : Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / by Gordon Slade ; edited by Jean Picard
(École d'Été de Probabilités de Saint-Flour ; 1879)

Edition	1st ed. 2006.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2006
Language	English
Size	XIII, 233 p : online resource
Authors	*Slade, Gordon author Picard, Jean editor SpringerLink (Online service)
Subjects	LCSH:Probabilities LCSH:Mathematical physics LCSH:Discrete mathematics FREE:Probability Theory FREE:Theoretical, Mathematical and Computational Physics FREE:Discrete Mathematics
Notes	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 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 HTTP:URL=https://doi.org/10.1007/b128444

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