03972nam 22007575 450 991025429420332120230810190309.03-319-43476-410.1007/978-3-319-43476-6(CKB)3710000001041181(DE-He213)978-3-319-43476-6(MiAaPQ)EBC6315739(MiAaPQ)EBC5577663(Au-PeEL)EBL5577663(OCoLC)972330747(PPN)198341482(EXLCZ)99371000000104118120170130d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierDiscrete Probability Models and Methods Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding /by Pierre Brémaud1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XIV, 559 p. 92 illus.) Probability Theory and Stochastic Modelling,2199-3149 ;783-319-43475-6 Includes bibliographical references and index.Introduction -- 1.Events and probability -- 2.Random variables -- 3.Bounds and inequalities -- 4.Almost-sure convergence -- 5.Coupling and the variation distance -- 6.The probabilistic method -- 7.Codes and trees -- 8.Markov chains -- 9.Branching trees -- 10.Markov fields on graphs -- 11.Random graphs -- 12.Recurrence of Markov chains -- 13.Random walks on graphs -- 14.Asymptotic behaviour of Markov chains -- 15.Monte Carlo sampling -- 16. Convergence rates -- Appendix -- Bibliography.The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book. .Probability Theory and Stochastic Modelling,2199-3149 ;78ProbabilitiesComputer scienceMathematicsMathematical statisticsGraph theoryCoding theoryInformation theoryComputer networksProbability TheoryProbability and Statistics in Computer ScienceGraph TheoryCoding and Information TheoryComputer Communication NetworksProbabilities.Computer scienceMathematics.Mathematical statistics.Graph theory.Coding theory.Information theory.Computer networks.Probability Theory.Probability and Statistics in Computer Science.Graph Theory.Coding and Information Theory.Computer Communication Networks.519.2Brémaud Pierreauthttp://id.loc.gov/vocabulary/relators/aut56619MiAaPQMiAaPQMiAaPQBOOK9910254294203321Discrete probability models and methods1560490UNINA