Continuum Percolation [Paperback]

A unified treatment of a spatial random process that can be used to model many natural phenomena.This book presents a unified account of current knowledge of the theory of continuum percolation, a kind of spatial random process that can be used to model many natural phenomena. The treatment is systematic and rigorous. Two models of continuum percolation are treated in detail and related models are discussed. All important techniques and methods are explained and applied. This self-contained book, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry.This book presents a unified account of current knowledge of the theory of continuum percolation, a kind of spatial random process that can be used to model many natural phenomena. The treatment is systematic and rigorous. Two models of continuum percolation are treated in detail and related models are discussed. All important techniques and methods are explained and applied. This self-contained book, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry.Many phenomena in physics, chemistry, and biology can be modeled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modeled is made up of individual events that overlap e.g., individual raindrops that eventually make the ground evenly wet. This is a systematic, rigorous account of continuum percolation. The authors treat two models, the Boolean model and the random connection model, in detail, and they discuss related continuum models. Meester and Roy explain all important techniques and methods and apply them to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models.Preface; 1. Introduction;l3&