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[美]T·M·里戈特(Thomas M.Liggett) 著 / 世界图书出版公司 / 2013-03 / 平装
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上书时间2023-10-16
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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.
FrequentlyUsedNotationIntroductionCHAPTERⅠTheConstruction,andOtherGeneralResults1.MarkovProcessesandTheirSemigroups2.SemigroupsandTheirGenerators3.TheConstructionofGeneratorsforParticleSystems4.ApplicationsoftheConstruction5.TheMartingaleProblem6.TheMartingaleProblemforParticleSystems7.Examples8.NotesandReferences9.OpenProblemsCHAPTERⅡSomeBasicTools1.Coupling2.MonotonicityandPositiveCorrelations3.Duality4.RelativeEntropy5.Reversibility6.RecurrenceandTransienceofReversibleMarkovChains7.SuperpositionsofCommutingMarkovChains8.PerturbationsofRandomWalks9.NotesandReferencesCHAPTERⅢSpinSystems1.CouplingsforSpinSystems2.AttractiveSpinSystems3.AttractiveNearest-NeighborSpinSystemsonZ14.DualityforSpinSystems5.ApplicationsofDuality6.AdditiveSpinSystemsandtheGraphicalRepresentation7.NotesandReferences8.OpenProblemsCHAPTERⅣStochasticIsingModels1.GibbsStates2.ReversibilityofStochasticIsingModels3.PhaseTransition4.L2Theory5.CharacterizationofInvariantMeasures6.NotesandReferences7.OpenProblemsCHAPTERⅤTheVoterModel1.ErgodicTheorems2.PropertiesoftheInvariantMeasures3.ClusteringinOneDimension4.TheFiniteSystem5.NotesandReferencesCHAPTERⅥTheContactProcess1.TheCriticalValue2.ConvergenceTheorems3.RatesofConvergence4.HigherDimensions5.NotesandReferences6.OpenProblemsCHAPTERⅦNearest-ParticleSystems1.ReversibleFiniteSystems2.GeneralFiniteSystems3.ConstructionofInfiniteSystems4.ReversibleInfiniteSystems5.GeneralInfiniteSystems6.NotesandReferences7.OpenProblemsCHAPTERⅧTheExclusionProcess1.ErgodicTheoremsforSymmetricSystems2.CouplingandInvariantMeasuresforGeneralSystems3.ErgodicTheoremsforTranslationInvariantSystems4.TheTaggedParticleProcess5.NonequilibriumBehavior6.NotesandReferences7.OpenProblemsCHAPTERⅨLinearSystemswithValuesin[0,oo)s1.TheConstruction;CouplingandDuality2.SurvivalandExtinction3.SurvivalviaSecondMoments4.ExtinctioninOneandTwoDimensions5.ExtinctioninHigherDimensions6.ExamplesandApplications7.NotesandReferences8.OpenProblemsBibliographyIndexPostfaceErrata
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