Slade, Gordon.
The Lace Expansion and its Applications Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / [electronic resource] : by Gordon Slade ; edited by Jean Picard. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006. - XIII, 233 p. online resource. - Lecture Notes in Mathematics, 1879 0075-8434 ; . - Lecture Notes in Mathematics, 1879 .
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.
9783540355182
10.1007/b128444 doi
Mathematics.
Combinatorics.
Distribution (Probability theory).
Mathematical physics.
Mathematics.
Probability Theory and Stochastic Processes.
Mathematical and Computational Physics.
Combinatorics.
QA273.A1-274.9 QA274-274.9
519.2
The Lace Expansion and its Applications Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 / [electronic resource] : by Gordon Slade ; edited by Jean Picard. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006. - XIII, 233 p. online resource. - Lecture Notes in Mathematics, 1879 0075-8434 ; . - Lecture Notes in Mathematics, 1879 .
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.
9783540355182
10.1007/b128444 doi
Mathematics.
Combinatorics.
Distribution (Probability theory).
Mathematical physics.
Mathematics.
Probability Theory and Stochastic Processes.
Mathematical and Computational Physics.
Combinatorics.
QA273.A1-274.9 QA274-274.9
519.2