Percolation /
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...
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
1989.
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xi, 296 pages) |
| ISBN: | 9781475742084 (electronic bk.) 1475742088 (electronic bk.) |