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| 內容簡介： |
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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.
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| 目錄：
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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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