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The Lace Expansion and its Applications [electronic resource] : Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / by Gordon Slade ; edited by Jean Picard.

By: Slade, Gordon [author.].
Contributor(s): Picard, Jean [editor.] | SpringerLink (Online service).
Material type: TextTextSeries: École d'Été de Probabilités de Saint-Flour: 1879Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006Description: XIII, 233 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540355182.Subject(s): Distribution (Probability theory | Combinatorics | Probability Theory and Stochastic Processes | Theoretical, Mathematical and Computational Physics | CombinatoricsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 519.2 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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