高维凸粒布尔模型中的渗流

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2023-01-01 DOI:10.1214/23-ejp997

Jean-Baptiste Gouéré, Florestan Labéy

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引用次数: 0

摘要

研究了高维凸粒布尔模型中的渗流问题。对于每个维d，固定一个内部不空的紧致、凸和对称集合K∧Rd。在第一种情况下，布尔模型是K的平移量的集合。在第二种情况下，布尔模型是更进一步的参数ρ∈(1,2)的K或ρK的平移量的集合。在这两种情况下，给出了渗透概率和渗透阈值的渐近性质。

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Percolation in the Boolean model with convex grains in high dimension

We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K⊂Rd with non empty interior. In a first setting, the Boolean model is a reunion of translates of K. In a second setting, the Boolean model is a reunion of translates of K or ρK for a further parameter ρ∈(1,2). We give the asymptotic behavior of the percolation probability and of the percolation threshold in the two settings.

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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.