This book presents a unified account of continuum percolation, a spatial random process that can be used to model many natural phenomena. The treatment is self-contained, assuming only familiarity with measure theory and basic probability theory. It will appeal to students and researchers in probability and stochastic geometry.
Inhaltsverzeichnis
Preface; 1. Introduction; 2. Basic methods; 3. Occupancy in Poisson Boolean models; 4. Vacancy in Poisson Boolean models; 5. Distinguishing features of the Poisson Boolean model; 6. The Poisson random-connection model; 7. Models driven by general processes; 8. Other continuum percolation models; References; Index.
Klappentext
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.
