Combinatorial Stochastic Processes : Ecole d'Etï½ de Probabilitï½s de Saint-Flour XXXII - 2002 - Jim Pitman

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Combinatorial Stochastic Processes

Ecole d'Etï½ de Probabilitï½s de Saint-Flour XXXII - 2002

By: Jim Pitman, Jean Picard (Editor)

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Paperback | 11 May 2006

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Three 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

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"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)

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Probability & Statistics Combinatorics & Graph Theory Discrete Mathematics

Preliminaries	p. 1
Preface	p. 1
Introduction	p. 2
Brownian motion and related processes	p. 3
Subordinators	p. 9
Bell polynomials and Gibbs partitions	p. 13
Notation	p. 14
Partitions and compositions	p. 14
Moments and cumulants	p. 20
Random sums	p. 23
Gibbs partitions	p. 24
Exchangeable random partitions	p. 37
Finite partitions	p. 38
Infinite partitions	p. 42
Structural distributions	p. 46
Convergence	p. 48
Limits of Gibbs partitions	p. 50
Sequential constructions of random partitions	p. 55
The Chinese restaurant process	p. 56
The two-parameter model	p. 60
Asymptotics	p. 67
A branching process construction	p. 72
Poisson constructions of random partitions	p. 77
Size-biased sampling	p. 78
Poisson representation of the two-parameter model	p. 81
Representation of infinite Gibbs partitons	p. 85
Lengths of stable excursions	p. 87
Brownian excursions	p. 90
Coagulation and fragmentation processes	p. 97
Coalescents	p. 98
Fragmentations	p. 106
Representations of infinite partitions	p. 109
Coagulation and subordination	p. 112
Coagulation-fragmentation duality	p. 116
Random walks and random forests	p. 121
Cyclic shifts and Lagrange inversion	p. 122
Galton-Watson forests	p. 125
Brownian asymptotics for conditioned Galton-Watson trees	p. 129
Critical random graphs	p. 135
The Brownian forest	p. 143
Plane trees with edge-lengths	p. 144
Binary Galton-Watson trees	p. 146
Trees in continuous paths	p. 149
Brownian trees and excursions	p. 152
Plane forests with edge-lengths	p. 162
Sampling at downcrossing times	p. 165
Sampling at Poisson times	p. 167
Path decompositions	p. 172
Further developments	p. 174
Brownian local times	p. 177
Stopping at an inverse local time	p. 177
Squares of Bessel processes	p. 179
Stopping at fixed times	p. 182
Time-changed local time processes	p. 185
Branching process approximations	p. 187
Brownian bridge asymptotics	p. 193
Basins and trees	p. 194
Mapping walks	p. 198
Brownian asymptotics	p. 199
The diameter	p. 203
The height profile	p. 205
Non-uniform random mappings	p. 206
Random forests and the additive coalescent	p. 207
Random p-forests and Cayley's multinomial expansion	p. 208
The additive coalescent	p. 210
The standard additive coalescent	p. 213
Poisson cutting of the Brownian tree	p. 215
Bibliography	p. 223
Index	p. 249
List of participants	p. 253
List of short lectures	p. 255
Table of Contents provided by Ingram. All Rights Reserved.

Combinatorial Stochastic Processes

Ecole d'Etï½ de Probabilitï½s de Saint-Flour XXXII - 2002

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Paperback

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