Abstract:
A study is made of a duality problem for percolation of a continuous random field
in a plane rectangle. This problem arose in physics in connection with the study
of critical phenomena in disordered systems. A duality theorem which is stated
and proved improves the theorem that exists in the physical literature for smooth
random fields.
Citation:
A. K. Stepanov, “Duality principle for percolation in random fields on a plane”, TMF, 67:1 (1986), 32–39; Theoret. and Math. Phys., 67:1 (1986), 339–343
\Bibitem{Ste86}
\by A.~K.~Stepanov
\paper Duality principle for percolation in random fields on a~plane
\jour TMF
\yr 1986
\vol 67
\issue 1
\pages 32--39
\mathnet{http://mi.mathnet.ru/tmf4918}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=843797}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 67
\issue 1
\pages 339--343
\crossref{https://doi.org/10.1007/BF01028886}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1986E968100004}
Linking options:
https://www.mathnet.ru/eng/tmf4918
https://www.mathnet.ru/eng/tmf/v67/i1/p32
This publication is cited in the following 2 articles:
A.K. Stepanov, “Failure criterion of a solid with a hierarchy of defects of the same physical type”, Theoretical and Applied Fracture Mechanics, 29:3 (1998), 219
S. A. Molchanov, A. K. Stepanov, “Percolation in random fields. III”, Theoret. and Math. Phys., 67:2 (1986), 434–439
Citation in format AMSBIB
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