Geodesic
Hierarchical models in discrete percolation theory and Markov branching processes
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 235 (2024), pp. 15-33

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
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     title = {Hierarchical models in discrete percolation theory and {Markov} branching processes},
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Yu. P. Virchenko; D. A. Cherkashin. Hierarchical models in discrete percolation theory and Markov branching processes. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 235 (2024), pp. 15-33. http://geodesic.mathdoc.fr/item/INTO_2024_235_a1/