The lace expansion and its applications : Ecole d'Eté de Probabilités de Saint-Flour XXXIV-2004 / G. Slade ; editor, Jean Picard.

By: Slade, G. (Gordon)
Contributor(s): Picard, Jean, 1959- | Ecole d'été de probabilités de Saint-Flour (34th : 2004)
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1879.Publisher: Berlin : Springer, ©2006Description: 1 online resource (xiii, 228 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540355182; 3540355189; 3540311890; 9783540311898; 1280615001; 9781280615009Other title: Ecole d'Eté de Probabilités de Saint-Flour XXXIV-2004Subject(s): Percolation (Statistical physics) | Scaling laws (Statistical physics) | Mathematical statistics | Probabilities | Percolation (Physique statistique) | Lois d'échelle (Physique statistique) | Statistique mathématique | Probabilités | SCIENCE -- Physics -- General | Percolation (Statistical physics) | Scaling laws (Statistical physics) | Mathematical statistics | Probabilities | Mathematical statistics | Percolation (Statistical physics) | Probabilities | Scaling laws (Statistical physics) | Statistische mechanica | Expansies (wiskunde) | wiskunde | mathematics | fysica | physics | stochastische processen | stochastic processes | combinatoriek | combinatorics | computational science | waarschijnlijkheidstheorie | probability theory | Mathematics (General) | Wiskunde (algemeen)Genre/Form: Electronic books. | Conference papers and proceedings. Additional physical formats: Print version:: Lace expansion and its applications.DDC classification: 530.13 LOC classification: QC174.85.P45 | S57 2006ebOther classification: O414. 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.
Summary: 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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Includes bibliographical references and index.

Print version record.

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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