Probability on Discrete Structures / Edition 1

Probability on Discrete Structures / Edition 1

by David Aldous
     
 

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ISBN-10: 3540008454

ISBN-13: 9783540008453

Pub. Date: 11/05/2003

Publisher: Springer Berlin Heidelberg

Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and

Overview

Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.

Product Details

ISBN-13:
9783540008453
Publisher:
Springer Berlin Heidelberg
Publication date:
11/05/2003
Series:
Encyclopaedia of Mathematical Sciences Series, #110
Edition description:
2004
Pages:
351
Product dimensions:
6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

D. Aldous, J.M. Steele: The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence.- G. Grimmett: The Random-Cluster Model.- C.G. Howard: Models of First-Passage Percolation.- F. Martinelli: Relaxation Times of Markov Chains in Statistical Mechanics and Combinatorial Structures.- L. Saloff-Coste: Random Walks on Finite Groups.- Index.

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