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This book contains eleven articles surveying emerging topics in discrete probability. The papers are based on talks given by experts at the DIMACS "Microsurveys in Discrete Probability" workshop held at the Institute for Advanced Study, Princeton, NJ, in 1997. This compilation of current research in discrete probability provides a unique overview that is not available elsewhere in book or survey form.
Topics covered in the volume include: Markov chains (perfect sampling, coupling from the past, mixing times), random trees (spanning trees on infinite graphs, enumeration of trees and forests, tree-valued Markov chains), distributional estimates (method of bounded differences, Stein-Chen method for normal approximation), dynamical percolation, Poisson processes, and reconstructing random walk from scenery.
Foreword vii Preface ix Tree-valued Markov chains and Poisson-Galton-Watson distributions David Aldous 1 On the central role of scale invariant Poisson processes on (0, infinity) Richard Arratia 21 Beyond the method of bounded differences Anant P. Godbole and Pawel Hitczenko 43 Dynamical percolation: Early results and open problems Olle Häggström 59 Distinguishing and reconstructing sceneries from observations along random walk paths Harry Kesten 75 Mixing times Laszlo Lovász and Peter Winkler 85 A bird's-eye view of uniform spanning trees and forests Russell Lyons 135 Enumerations of trees and forests related to branching processes and random walks Jim Pitman 163 Coupling from the past: A user's guide James Propp and David Wilson 181 Couplings for normal approximations with Stein's method Gesine Reinert 193 Annotated bibliography of perfectly random sampling with Markov chains David B. Wilson 209