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Book
Combinatorial Stochastic Processes
(2006)
  • Jim Pitman, University of California, Berkeley
Abstract

This is a set of lecture notes for a course given at the St. Flour summer school in July 2002. The theme of the course is the study of various combinatorial models of random partitions and random trees, and the asymptotics of these models related to continuous parameter stochastic processes. Following is a list of the main topics treated: models for random combinatorial structures, such as trees, forests, permutations, mappings, and partitions; probabilistic interpretations of various combinatorial notions e.g. Bell polynomials, Stirling numbers, polynomials of binomial type, Lagrange inversion; Kingman's theory of exchangeable random partitions and random discrete distributions; connections between random combinatorial structures and processes with independent increments: Poisson-Dirichlet limits; random partitions derived from subordinators; asymptotics of random trees, graphs and mappings related to excursions of Brownian motion; continuum random trees embedded in Brownian motion; Brownian local times and squares of Bessel processes; various processes of fragmentation and coagulation, including Kingman's coalescent, the additive and multiplicative coalescents

Keywords
  • random trees,
  • random partitions,
  • coagulation,
  • fragmentation,
  • Gibbs distributions,
  • subordinator,
  • local time,
  • Brownian motion,
  • Bessel process
Disciplines
Publication Date
2006
Publisher
Springer-Verlag
Series
ecture Notes in Mathematics
ISBN
978-3-540-30990-1
Citation Information
Jim Pitman. Combinatorial Stochastic Processes . Berlin: Springer-Verlag, 2006. Available at: http://works.bepress.com/jim_pitman/1 and via SpringerLink