Percolation
By: by Geoffrey Grimmett
Publisher: Springer New York
Published: 1989
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 296
ISBN-13: 9781475742107; 9781475742084
Subjects: Mathematics; Distribution (Probability theory)
Description: The mathematical theory of percolation has acquired something of a reputation for inaccessibility. In addition, several recent advances of substance have tossed the historical order of discovery on its head. It is time to re-examine the subject afresh, in light of recent discoveries. This book does just that. It contains a definitive and coherent account of the subject, in an orderly way accessible to the non-specialist, including the shortest and neatest proofs currently known. In order to maximize accessibility, it concentrates on bond percolation on the d-dimensional cubic lattice where d>2. The subcritical and supercritical phases are described in considerable detail; the recent proofs of the uniqueness of critical points and the infinite open cluster are used extensively. There are two chapters devoted to a lucid account of the physical theory of scaling the renormalization in the context of percolation. There is a chapter dealing with the case of two dimensions, including a rather short proof of the famous exact calculation of + for the critical probability. The book terminates with a collection of pencil sketches of related areas of mathematics and physics.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.