逾渗（第2版）（英文版）

图书标准信息

• 作者 [英]格里密特（Grimmett G.） 著
• 出版社 世界图书出版公司
• 出版时间 2012-08
• 版次 2
• ISBN 9787510046292
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 444页
• 正文语种 英语

【内容简介】

Thisbookisaboutthemathematicsofpercolationtheory，withtheemphasisuponpresentingtheshortestrigorousproofsofthemainfacts.Ihavemadecertainsacrificesinordertomaximizetheaccessibilityofthetheory，andthemajoronehasbeentorestrictmyselfalmostentirelytothespecialcaseofbondpercolationonthecubiclatticeZd.Thusthereisonlylittlediscussionofsuchprocessesascontinuum，mixed，inhomogeneous，long-range，first-passage，andorientedpercolation.NorhaveIspentmuchtimeorspaceontherelationshipofpercolationtostatisticalphysics，infiniteparticlesystems，disorderedmedia，reliabilitytheory，andsoon.Withtheexceptionofthetwofinalchapters，Ihavetriedtostayreasonablyclosetocorematerialofthesortwhichmostgraduatestudentsintheareamightaspiretoknow.Nocriticalreaderwillagreeentirelywithmyselection，andphysicistsmaysometimesfeelthatmyintuitioniscrooked.

【目录】

1WhatisPercolation？
1.1ModellingaRandomMedium
1.2WhyPercolation？
1.3BondPercolation
1.4TheCriticalPhenomenon
1.5TheMainQuestions
1.6SitePercolation
1.7Notes

2SomeBasicTechniques
2.1IncreasingEvents
2.2TheFKGInequality
2.3TheBKInequality
2.4Russo'sFormula
2.5InequalitiesofReliabilityTheory
2.6AnotherInequality
2.7Notes

3CriticalProbabilities
3.1EqualitiesandInequalities
3.2StrictInequalities
3.3Enhancements
3.4BondandSiteCriticalProbabilities
3.5Notes

4TheNumberofOpenClustersperVertex
4.1Definition
4.2LatticeAnimalsandLargeDeviations
4.3DifferentiabilityofK
4.4Notes

5ExponentialDecay
5.1MeanClusterSize
5.2ExponentialDecayoftheRadiusDistributionbeneathPe
5.3UsingDifferentialInequalities
5.4Notes

6TheSubcriticalPhase
6.1TheRadiusofanOpenCluster
6.2ConnectivityFunctionsandCorrelationLength
6.3ExponentialDecayoftheClusterSizeDistribution
6.4AnalyticityofKandX
6.5Notes

7DynamicandStaticRenormalization
7.1PercolationinSlabs
7.2PercolationofBlocks
7.3PercolationinHalf-Spaces
7.4StaticRenormalization
7.5Notes

8TheSupercriticalPhase
8.1Introduction
8.2UniquenessoftheInfiniteOpenCluster
8.3ContinuityofthePercolationProbability
8.4TheRadiusofaFiniteOpenCluster
8.5TruncatedConnectivityFunctionsandCorrelationLength
8.6Sub-ExponentialDecayoftheClusterSizeDistribution
8.7Differentiabilityof
8.8GeometryoftheInfiniteOpenCluster
8.9Notes

9NeartheCriticalPoint：ScalingTheory
9.1PowerLawsandCriticalExponents
9.2ScalingTheory
9.3Renormalization
9.4TheIncipientInfiniteCluster
9.5Notes

10NeartheCriticalPoint：RigorousResults
10.1PercolationonaTree
10.2InequalitiesforCriticalExponents
10.3MeanFieldTheory
10.4Notes

11BondPercolationinTwoDimensions
12ExtensionsofPercolation
13PereolativeSystems
AppendixⅠTheInfinite-VolumeLimitforPercolation
AppendixⅡTheSubadditiveInequality
ListofNotation
References
IndexofNames
SubjectIndex