Limiting behavior of percolation cluster in a multilayered random environment with breakdown
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Vladimir I. Vinokurov
Abstract
We consider a sequence (n = 1, 2, ⋯) of finite Markov chains {ωn,t}t≥1 with discrete time describing the percolation process in a band of width n of a multilayered random medium in which a flow (breakdown) already exists, and random variable ωn,t equals to the width of the percolation cluster at time t. For each value of n and given random percolation mechanism the Markov chain {ωn,t}t≥1 has a limit stationary distribution, corresponding to the random variable ωn. In the case when the width n of the layers of the medium under consideration tends to infinity, the limit distribution of the random variables Ωn
Originally published in Diskretnaya Matematika (2024) 36, №2, 11–22 (in Russian).
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On continuants of continued fractions with rational partial quotients
- On linear equivalence of piecewise-linear permutations of the field 𝔽2n
- On the prospective minimum of the random walk conditioned to stay nonnegative
- Limiting behavior of percolation cluster in a multilayered random environment with breakdown
Artikel in diesem Heft
- Frontmatter
- On continuants of continued fractions with rational partial quotients
- On linear equivalence of piecewise-linear permutations of the field 𝔽2n
- On the prospective minimum of the random walk conditioned to stay nonnegative
- Limiting behavior of percolation cluster in a multilayered random environment with breakdown
