文章基本信息

标题：Lipschitz percolation
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作者：Dirr, Nicolas ; Dondl, Patrick W. ; Grimmett, Geoffrey R. 等
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2010
卷号：15
页码：14-21
DOI：10.1214/ECP.v15-1521
出版社：Electronic Communications in Probability
摘要：We prove the existence of a (random) Lipschitz function $F:\mathbb{Z}^{d-1}\to\mathbb{Z}^+$ such that, for every $x\in\mathbb{Z}^{d-1}$, the site $(x,F(x))$ is open in a site percolation process on $\mathbb{Z}^{d}$. The Lipschitz constant may be taken to be $1$ when the parameter $p$ of the percolation model is sufficiently close to $1$.
关键词：percolation, Lipschitz embedding, random surface;60K35, 82B20