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作者[美]T·M·里戈特(Thomas M.Liggett) 著
出版社世界图书出版公司
出版时间2013-03
版次1
装帧平装
上书时间2024-08-22
商品详情
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图书标准信息
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作者
[美]T·M·里戈特(Thomas M.Liggett) 著
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出版社
世界图书出版公司
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出版时间
2013-03
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版次
1
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ISBN
9787510058097
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定价
79.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
496页
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正文语种
英语
- 【内容简介】
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Myintentionisthatthisbookserveasareferenceworkoninteractingparticlesystems,andthatitbeusedasthebasisforanadvancedgraduatecourseonthissubject.Thebookshouldbeofinterestnotonlytomathematicians,butalsotoworkersinrelatedareassuchasmathematicalphysicsandmathematicalbiology.Theprerequisitesforreadingitaresolidone-yeargraduatecoursesinanalysisandprobabilitytheory,atthelevelofRoyden(1968)andChung(1974),respectively.Materialwhichisusuallycoveredinthesecourseswillbeusedwithoutcomment.Inaddition,afamiliaritywithanumberofothertypesofstochasticprocesseswillbehelpful.However,referenceswillbegivenwhenresultsfromspecializedpartsofprobabilitytheoryareused.Noparticularknowledgeofstatisticalmechanicsormathematicalbiologyisassumed.Whilethisisthefirstbook-lengthtreatmentofthesubjectofinteractingparticlesystems,anumberofsurveysofpartsofthefieldhaveappearedinrecentyears.AmongtheseareSpitzer(1974a),Holley(1974a),Sullivan(1975b),Liggett(1977b),Stroock(1978),Griffeath(1979a,1981),andDurrett(1981).Thesecanserveasusefulcomolementstotheoresentwork.
- 【目录】
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FrequentlyUsedNotation
Introduction
CHAPTERⅠ
TheConstruction,andOtherGeneralResults
1.MarkovProcessesandTheirSemigroups
2.SemigroupsandTheirGenerators
3.TheConstructionofGeneratorsforParticleSystems
4.ApplicationsoftheConstruction
5.TheMartingaleProblem
6.TheMartingaleProblemforParticleSystems
7.Examples
8.NotesandReferences
9.OpenProblems
CHAPTERⅡ
SomeBasicTools
1.Coupling
2.MonotonicityandPositiveCorrelations
3.Duality
4.RelativeEntropy
5.Reversibility
6.RecurrenceandTransienceofReversibleMarkovChains
7.SuperpositionsofCommutingMarkovChains
8.PerturbationsofRandomWalks
9.NotesandReferences
CHAPTERⅢ
SpinSystems
1.CouplingsforSpinSystems
2.AttractiveSpinSystems
3.AttractiveNearest-NeighborSpinSystemsonZ1
4.DualityforSpinSystems
5.ApplicationsofDuality
6.AdditiveSpinSystemsandtheGraphicalRepresentation
7.NotesandReferences
8.OpenProblems
CHAPTERⅣ
StochasticIsingModels
1.GibbsStates
2.ReversibilityofStochasticIsingModels
3.PhaseTransition
4.L2Theory
5.CharacterizationofInvariantMeasures
6.NotesandReferences
7.OpenProblems
CHAPTERⅤ
TheVoterModel
1.ErgodicTheorems
2.PropertiesoftheInvariantMeasures
3.ClusteringinOneDimension
4.TheFiniteSystem
5.NotesandReferences
CHAPTERⅥ
TheContactProcess
1.TheCriticalValue
2.ConvergenceTheorems
3.RatesofConvergence
4.HigherDimensions
5.NotesandReferences
6.OpenProblems
CHAPTERⅦ
Nearest-ParticleSystems
1.ReversibleFiniteSystems
2.GeneralFiniteSystems
3.ConstructionofInfiniteSystems
4.ReversibleInfiniteSystems
5.GeneralInfiniteSystems
6.NotesandReferences
7.OpenProblems
CHAPTERⅧ
TheExclusionProcess
1.ErgodicTheoremsforSymmetricSystems
2.CouplingandInvariantMeasuresforGeneralSystems
3.ErgodicTheoremsforTranslationInvariantSystems
4.TheTaggedParticleProcess
5.NonequilibriumBehavior
6.NotesandReferences
7.OpenProblems
CHAPTERⅨ
LinearSystemswithValuesin[0,oo)s
1.TheConstruction;CouplingandDuality
2.SurvivalandExtinction
3.SurvivalviaSecondMoments
4.ExtinctioninOneandTwoDimensions
5.ExtinctioninHigherDimensions
6.ExamplesandApplications
7.NotesandReferences
8.OpenProblems
Bibliography
Index
Postface
Errata
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