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Teoreticheskaya i Matematicheskaya Fizika, 1985, Volume 62, Number 2, Pages 253–262 (Mi tmf4565)  

This article is cited in 9 scientific papers (total in 9 papers)

Continuous models of percolation theory. II

S. A. Zuev, A. F. Sidorenko
References:
Abstract: Percolation models in which the centers of defects are distributed randomly in space in accordance with Poisson's law and the shape of each defect is also random are considered. Methods of obtaining rigorous estimates of the critical densities are described. It is shown that the number of infinite clusters can take only three values: 0, 1, or $\infty$. Models in which the defects have an elongated shape and a random orientation are investigated in detail. In the two-dimensional case, it is shown that the critical volume concentration of the defects is proportional to $a/l$, where $l$ and $a$ are, respectively, the major and minor axes of the defect; the mean number of (direct) bonds per defect when percolation occurs is bounded.
Received: 29.03.1984
English version:
Theoretical and Mathematical Physics, 1985, Volume 62, Issue 2, Pages 171–177
DOI: https://doi.org/10.1007/BF01033527
Bibliographic databases:
Language: Russian
Citation: S. A. Zuev, A. F. Sidorenko, “Continuous models of percolation theory. II”, TMF, 62:2 (1985), 253–262; Theoret. and Math. Phys., 62:2 (1985), 171–177
Citation in format AMSBIB
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\by S.~A.~Zuev, A.~F.~Sidorenko
\paper Continuous models of percolation theory.~II
\jour TMF
\yr 1985
\vol 62
\issue 2
\pages 253--262
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=783056}
\transl
\jour Theoret. and Math. Phys.
\yr 1985
\vol 62
\issue 2
\pages 171--177
\crossref{https://doi.org/10.1007/BF01033527}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1985ARH5400008}
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  • https://www.mathnet.ru/eng/tmf4565
  • https://www.mathnet.ru/eng/tmf/v62/i2/p253
    Cycle of papers
    This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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