Combinatorial Stochastic Processes
BeschreibungThe purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes, in particular the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes. The course is a summary and review of the author's research over the last ten years, much of it joint work with coauthors David Aldous, Jean Bertoin, Steven Evans, and Marc Yor.
InhaltsverzeichnisPreliminaries.- Bell polynomials, composite structures and Gibbs partitions.- Exchangeable random partitions.- Sequential constructions of random partitions.- Poisson constructions of random partitions.- Coagulation and fragmentation processes.- Random walks and random forests.- The Brownian forest.- Brownian local times, branching and Bessel processes.- Brownian bridge asymptotics for random mappings.- Random forests and the additive coalescent.
PortraitJim Pitman is a Professor of Mathematics and Statistics at the University of California, Berkeley, where he has been employed since 1978. He attended the Australian National University and The University of Sheffield.
PressestimmenFrom the reviews:
"The intertwining of many aspects of combinatorics and probability is treated in the book under review. ... I think this is an important book for a variety of mathematicians. Moreover, the good exercises provided in each section and a good bibliography make the book suitable as a textbook for topics courses and as a reference for particular topics in various standard courses." (Bert Fristedt, Mathematical Reviews, Issue 2008 c)
Untertitel: Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002. 'Lecture Notes in Mathematics'. 2006. Auflage. 16 schwarz-weiße Abbildungen, 1 schwarz-weiße Tabellen, Bibliographie. Book. Sprache: Englisch.
Verlag: Springer-Verlag GmbH
Erscheinungsdatum: Mai 2006