Combinatorial Stochastic Processes: Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002Three series of lectures were given at the 32nd Probability Summer School in Saint-Flour (July 7–24, 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 |
Contents
0 Preliminaries | 1 |
Bell polynomials and Gibbs partitions | 12 |
Exchangeable random partitions | 37 |
Sequential constructions of random partitions | 54 |
Poisson constructions of random partitions | 77 |
Coagulation and fragmentation processes | 96 |
Random walks and random forests | 121 |
The Brownian forest | 143 |
Brownian local times | 176 |
Brownian bridge asymptotics | 193 |
Random forests and the additive coalescent | 207 |
Bibliography | 221 |
Other editions - View all
Combinatorial Stochastic Processes: Ecole d'Eté de Probabilités de Saint ... Jim Pitman Limited preview - 2006 |
Combinatorial Stochastic Processes: Ecole d'Eté de Probabilités de Saint ... Jim Pitman No preview available - 2006 |
Combinatorial Stochastic Processes: Ecole d'Eté de Probabilités de Saint ... Jim Pitman No preview available - 2009 |
Common terms and phrases
additive coalescent Aldous asymptotic Bertoin BESQ Bessel process binary branching process Brownian bridge Brownian excursion Brownian motion Brownian tree coagulation coalescent process combinatorial conditioned construction converges in distribution Corollary corresponding defined denote density depth-first search derived edges EPPF exchangeable partition exchangeable random partition Exercise F Univ finite formula fragmentation process function Galton-Watson trees Gibbs given Harris path II(t increments independent and identically infinite interval partition kernel Lemma Lévy Lévy processes Markov chain Markov process Math multiplicative coalescent non-negative Notes and comments offspring distribution P₁ PD(a Pitman plane forest plane tree Poisson process polynomials probabilistic probability distribution Proof random forest random mapping random permutation random trees random variables random walk ranked frequencies representation sampling self-similar size-biased standard Brownian Stirling numbers Stochastic structure subtrees Theorem theory tree components trees labeled uniform random vertex vertices