E-raamat: Continuum Percolation

Treats the Boolean and the random connection models of continuum percolation, which is used in spatial random processes. Explains the important techniques and methods to obtain results on the existence of phase transitions, the continuity of critical densities with respect to distribution, and other factors. Assumes a familiarity with measure theory and basic probability theory; the simple ergodic theory used should be comprehensible to anyone knowing basic geometry. Annotation c. by Book News, Inc., Portland, Or.

A unified treatment of a spatial random process that can be used to model many natural phenomena.

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.