Bollob?s B., Riordan O. Percolation

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размер 4.83 МБ
добавлен 24 октября 2011 г.

Издательство Cambridge University Press, 2006, -336 pp.
Качество среднее (бледный текст).
Percolation theory was founded by Broadbent and Hammersley almost half a century ag: by now thousands of papers and many books have been devoted to the subject. The original aim was to open up to mathematical analysis the study of random physical processes such as the flow of through a disorders porous medium. These problems in applied mathematics have attracted attention of many physicists as well as pure mathematicians, and have led to the accumulation of much experimental and heuristic evidence for many remarkable phenomena. Mathematically, the subject has tued out to be much more difficult than might have been expected, with several deep results and many more conjectured.
Basic concepts and results.
Probabilistic tools.
Boud percolation on Z² - the Harris-Kestell Theorem.
Exponential decay and critical probabilities – theorems of Menshikov and Aizenman & Barsky.
Uniqueness of the infinite open cluster and critical probabilities.
Estimating critical probabilities.
Conformal invariance - Smiov's Theorem.
Continuum pelcolation.

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