Continuum percolation
By: Ronald Meester, Rahul Roy.
Contributors: Roy, Rahul.
Series: Cambridge tracts in mathematics ;; 119
Publisher: Cambridge University Press
Published: 1996
Place of publication: Cambridge; New York
Language: eng
Number of pages: 238
Subjects: Percolation (Statistical physics); Stochastic processes.
Description: 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 (p. 233-235) and index.