| Description |
1 online resource (xiii, 228 pages) : illustrations |
| Series |
Lecture notes in mathematics, 0075-8434 ; 1879 |
|
Lecture notes in mathematics (Springer-Verlag) ; 1879.
|
| 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 |
| Analysis |
wiskunde |
|
mathematics |
|
fysica |
|
physics |
|
stochastische processen |
|
stochastic processes |
|
combinatoriek |
|
combinatorics |
|
computational science |
|
waarschijnlijkheidstheorie |
|
probability theory |
|
Mathematics (General) |
|
Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
|
Print version record |
| Subject |
Percolation (Statistical physics)
|
|
Scaling laws (Statistical physics)
|
|
Mathematical statistics.
|
|
Probabilities.
|
|
Probability
|
|
probability.
|
|
SCIENCE -- Physics -- General.
|
|
Percolation (Statistical physics)
|
|
Scaling laws (Statistical physics)
|
|
Mathematical statistics.
|
|
Probabilities.
|
|
Estadística matemática
|
|
Probabilidades
|
|
Mathematical statistics
|
|
Percolation (Statistical physics)
|
|
Probabilities
|
|
Scaling laws (Statistical physics)
|
|
Statistische mechanica.
|
|
Expansies (wiskunde)
|
| Genre/Form |
Conference papers and proceedings
|
| Form |
Electronic book
|
| Author |
Picard, Jean, 1959-
|
|
Ecole d'été de probabilités de Saint-Flour (34th : 2004)
|
| ISBN |
9783540355182 |
|
3540355189 |
|
3540311890 |
|
9783540311898 |
|
1280615001 |
|
9781280615009 |
|
