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Combinatorial Stochastic Processes:Ecole D'Ete de Probabilites de Saint-Flour, 2002 Vol.32

Combinatorial Stochastic Processes:Ecole D'Ete de Probabilites de Saint-Flour, 2002 Vol.32

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  • ISBN:9783540309901
  • Editorial: Springer Verlag
  • Fecha de la edición:
  • Colección: Lecture Notes in Mathematics Series nº 1875
  • Encuadernación:Tapa dura
  • Dimensiones: 0 cm x 0 cm
  • Nº Pág.:268
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The 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.

Preliminaries.- 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.- Bibliography.- Index.

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