Combinatorial Stochastic Processes

Three series of lectures were given at the 32nd Probability Summer School in Saint-Flour (July 724, 2002), by the Professors Pitman, Tsirelson and Werner. ThecoursesofProfessorsTsirelson(Scalinglimit,noise,stability)andWerner (Random planar curves and Schramm-Loewner evolutions) have been p- lished in a previous issue ofLectures Notes in Mathematics (volume 1840). This volume contains the course Combinatorial stochastic processes of Professor Pitman. We cordially thank the author for his performance in Saint-Flour and for these notes. 76 participants have attended this school. 33 of them have given a short lecture. The lists of participants and of short lectures are enclosed at the end of the volume. The Saint-Flour Probability Summer School was founded in 1971. Here are the references of Springer volumes which have been published prior to this one. All numbers refer to theLecture Notes in Mathematics series,except S-50 which refers to volume 50 of the Lecture Notes in Statistics series. 1971: vol 307 1980: vol 929 1990: vol 1527 1998: vol 1738 1973: vol 390 1981: vol 976 1991: vol 1541 1999: vol 1781 1974: vol 480 1982: vol 1097 1992: vol 1581 2000: vol 1816 1975: vol 539 1983: vol 1117 1993: vol 1608 2001: vol 1837 & 1851 1976: vol 598 1984: vol 1180 1994: vol 1648 2002: vol 1840 1977: vol 678 1985/86/87: vol 1362 & S-50 1995: vol 1690 2003: vol 1869 1978: vol 774 1988: vol 1427 1996: vol 1665 1979: vol 876 1989: vol 1464 1997: vol 1717

From 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)

Auteur

Jim 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.

Contenu
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.