文章基本信息

标题：Poisson percolation on the square lattice
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作者：Irina Cristali ; Matthew Junge ; Rick Durrett 等
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：1
页码：429-437
DOI：10.30757/ALEA.v16-16
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Suppose that on the square lattice the edge with midpoint x becomesopen at rate kxk􀀀1 . Let (x; t) be the probability that the corresponding edgeis open at time t and let n(p; t) be the distance at which edges are open withprobability p at time t. We show that with probability tending to 1 as t ! 1:(i) the open cluster containing the origin C0(t) is contained in the square of radiusn(pc􀀀; t), and (ii) the cluster lls the square of radius n(pc+; t) with the densityof points near x being close to ((x; t)) where (p) is the percolation probabilitywhen bonds are open with probability p on Z2. Results of Nolin suggest that ifN = n(pc; t) then the boundary uctuations of C0(t) are of size N4=7.