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Probability on Discrete Structures (Paperback, Softcover reprint of hardcover 1st ed. 2004)
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Probability on Discrete Structures (Paperback, Softcover reprint of hardcover 1st ed. 2004)
Series: Encyclopaedia of Mathematical Sciences, 110
Expected to ship within 10 - 15 working days
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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.
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