Continuum percolation / Ronald Meester, Rahul Roy

While much of the motivation for mathematical percolation theory has come from problems in continuous random media, most of the mathematical research in the subject has been concerned with lattice models. However, questions in the continuum have been of growing interest to mathematicians. Meester and Roy's book is the first to be devoted to these developments.
Much of the book is concerned with the so-called Boolean model, in which balls of random radii are centered at the points of a spatial Poisson process. The components of the union of the balls are the "occupied clusters''; "vacant clusters'' are also considered, and often require a treatment different from that of the occupied clusters; this is one special feature of continuum models. The book also discusses the so-called random connection model, in which each pair of points is connected with probability depending on their separation, inducing a random graph whose components are "clusters''. A further chapter is concerned with generalizing from the Poisson process to more general stationary point processes. A variety of other models are also briefly discussed. ... (MathSciNet)

Bibliogr. p. 233-235. Index