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Percolation theory and some applications

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Abstract

The goal of the survey is to present mathematically rigorous results obtained in the recent years in the new mathematical discipline: percolation theory, which is on the border between the theory of random fields, stochastic geometry, and mathematical physics. Here not only classical percolation schemes are considered (bond and site problems on lattices) but also various generalizations that arose in connection with actual physical applications.

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Authors
  1. M. V. Men'shikov
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  2. S. A. Molchanov
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  3. A. F. Sidorenko
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Translated from Itogi Nauki i Tekhniki, Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 24, pp. 53–110, 1986.

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Men'shikov, M.V., Molchanov, S.A. & Sidorenko, A.F. Percolation theory and some applications. J Math Sci 42, 1766–1810 (1988). https://doi.org/10.1007/BF01095508

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