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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2024, Volume 235, Pages 15–33
DOI: https://doi.org/10.36535/2782-4438-2024-235-15-33 (Mi into1305) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Hierarchical models in discrete percolation theory and Markov branching processes

Yu. P. Virchenko, D. A. Cherkashin

Belgorod Shukhov State Technological University
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DOI: https://doi.org/10.36535/2782-4438-2024-235-15-33
Abstract: A brief introduction to percolation theory is given. Within the framework of the discrete percolation theory on infinite graphs, we develop a method for approximating the percolation probability based on the construction of a sequence of infinite graphs of a special type called the hierarchical graphs. The calculation of the percolation probability for graphs of this type is reduced to the analysis of a suitable Markov branching process with discrete time.
Keywords: infinite graph, percolation probability, branching random process, supercritical regime, connectedness relation
Document Type: Article
UDC: 519.24
MSC: 60K35, 60J85
Language: Russian
Citation: Yu. P. Virchenko, D. A. Cherkashin, “Hierarchical models in discrete percolation theory and Markov branching processes”, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 235, VINITI, Moscow, 2024, 15–33
Citation in format AMSBIB
\Bibitem{VirChe24}
\by Yu.~P.~Virchenko, D.~A.~Cherkashin
\paper Hierarchical models in discrete percolation theory and Markov branching processes
\inbook Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2024
\vol 235
\pages 15--33
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1305}
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