TY - BOOK ID - 5451302 TI - The lace expansion and its applications : Ecole d'Ete de Probabilites de Saint-Flour XXXIV-2004 AU - Slade, G. AU - Picard, Jean PY - 2006 SN - 9783540311898 3540311890 9786610615001 1280615001 3540355189 PB - Berlin ; Heidelberg : Springer, DB - UniCat KW - Percolation (Statistical physics) KW - Scaling laws (Statistical physics) KW - Mathematical statistics. KW - Probabilities. KW - Percolation (Physique statistique) KW - Lois d'échelle (Physique statistique) KW - Statistique mathématique KW - Probabilités KW - Electronic books. -- local. KW - Percolation (Statistical physics). KW - Scaling laws (Statistical physics). KW - Mathematical statistics KW - Probabilities KW - Physics KW - Mathematics KW - Physical Sciences & Mathematics KW - Mathematical Theory KW - Mathematical Statistics KW - Atomic Physics KW - Probability KW - Statistical inference KW - Statistics, Mathematical KW - Ratio and proportion (Statistical physics) KW - Scale invariance (Statistical physics) KW - Scaling hypothesis (Statistical physics) KW - Scaling phenomena (Statistical physics) KW - Statistical methods KW - Mathematics. KW - Combinatorics. KW - Physics. KW - Probability Theory and Stochastic Processes. KW - Theoretical, Mathematical and Computational Physics. KW - Combinations KW - Chance KW - Least squares KW - Risk KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Combinatorics KW - Algebra KW - Mathematical analysis KW - Math KW - Science KW - Physical laws KW - Ranking and selection (Statistics) KW - Statistical physics KW - Statistics KW - Sampling (Statistics) KW - Lattice theory KW - Distribution (Probability theory. KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Mathematical physics. KW - Physical mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:5451302 AB - 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. ER -