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Microsurveys in Discrete Probability
Edited by: David Aldous, University of California, Berkeley, CA, and James Propp, University of Wisconsin, Madison, WI
A co-publication of the AMS and DIMACS.
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DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
1998; 220 pp; hardcover
Volume: 41
ISBN-10: 0-8218-0827-3
ISBN-13: 978-0-8218-0827-6
List Price: US$47
Member Price: US$37.60
Order Code: DIMACS/41
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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. 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, and Poisson processes.

Features:

  • surveys written and refereed by experts
  • emerging areas of research in discrete probability theory not previously surveyed
  • articles accessible to a broad readership

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).

Readership

Graduate students and researchers in probability and discrete mathematics and theoretical computer scientists.

Reviews

"This book contains several truly excellent surveys in discrete applied probability. The editors have done a splendid job of getting well-written articles, and this is well worth the price. The idea of publishing good up-to-date surveys is commendable."

-- Journal of the American Statistical Association

Table of Contents

  • D. Aldous -- Tree-valued Markov chains and Poisson-Galton-Watson distributions
  • R. Arratia -- On the central role of scale invariant Poisson processes on \((0, \infty)\)
  • A. P. Godbole and P. Hitczenko -- Beyond the method of bounded differences
  • O. Häggström -- Dynamical percolation: Early results and open problems
  • H. Kesten -- Distinguishing and reconstructing sceneries from observations along random walk paths
  • L. Lovász and P. Winkler -- Mixing times
  • R. Lyons -- A bird's-eye view of uniform spanning trees and forests
  • J. Pitman -- Enumerations of trees and forests related to branching processes and random walks
  • J. Propp and D. Wilson -- Coupling from the past: A user's guide
  • G. Reinert -- Couplings for normal approximations with Stein's method
  • D. B. Wilson -- Annotated bibliography of perfectly random sampling with Markov chains
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