Geodesic
Limiting behavior of percolation cluster in a multilayered random environment with breakdown
Diskretnaya Matematika, Tome 36 (2024) no. 2, pp. 11-22 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a sequence ($n=1,2,\cdots$) of finite Markov chains $\{\omega_{n,t}\}_{t\geq1}$ 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 $\omega_{n,t}$ equals to the width of the percolation cluster at time $t$. For each value of $n$ and given random percolation mechanism the Markov chain $\{\omega_{n,t}\}_{t\geq 1}$ has a limit stationary distribution, corresponding to the random variable $\omega_n$. 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 $\Omega_{n}\sqrt{b/n}$ ($b$ is some constant) is found, which is the Rayleigh distribution.
Keywords: percolation, percolation cluster, stationary distributions, limit theorems, Rayleigh distribution, method of moments.
Mots-clés : Markov chains 
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     author = {V. I. Vinokurov},
     title = {Limiting behavior of percolation cluster in a multilayered random environment with breakdown},
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V. I. Vinokurov. Limiting behavior of percolation cluster in a multilayered random environment with breakdown. Diskretnaya Matematika, Tome 36 (2024) no. 2, pp. 11-22. http://geodesic.mathdoc.fr/item/DM_2024_36_2_a1/

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