Continuum percolation / Ronald Meester, Rahul Roy.

Format:

Book

Author/Creator:

Meester, Ronald.

Contributor:

Roy, Rahul.

Series:

Cambridge tracts in mathematics ; 119.

Cambridge tracts in mathematics

Language:

English

Subjects (All):

Percolation (Statistical physics).

Stochastic processes.

Physical Description:

x, 238 pages : illustrations ; 23 cm.

Place of Publication:

Cambridge ; New York, NY, USA : Cambridge University Press, [1996]

Summary:

This book is the first systematic and rigorous account of continuum percolation. The authors treat two models, the Boolean model and the random connection model, in detail and discuss a number of related continuum models. Where appropriate, they make clear connections between discrete percolation and continuum percolation. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality of certain critical densities, continuity of critical densities with respect to distributions, uniqueness of the unbounded component, covered volume fractions, compression, rarefaction, and so on. The book is self-contained, assuming familiarity only with measure theory and basic probability theory. The approach makes use of simple ergodic theory, but the underlying geometric ideas are always made clear. Continuum Percolation will appeal to students and researchers in probability and stochastic geometry.

Notes:

Includes bibliographical references (pages 233-235) and index.

ISBN:

052147504X

OCLC:

33102408