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020 _a9783540355182
_9978-3-540-35518-2
024 7 _a10.1007/b128444
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aSlade, Gordon.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Lace Expansion and its Applications
_h[electronic resource] :
_bEcole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 /
_cby Gordon Slade ; edited by Jean Picard.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXIII, 233 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v1879
505 0 _aSimple 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.
520 _aThe 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.
650 0 _aDistribution (Probability theory.
650 0 _aCombinatorics.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
650 2 4 _aCombinatorics.
_0http://scigraph.springernature.com/things/product-market-codes/M29010
700 1 _aPicard, Jean.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540819516
776 0 8 _iPrinted edition:
_z9783540311898
830 0 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v1879
856 4 0 _uhttps://doi.org/10.1007/b128444
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10293
_d10293