From Greedy Lattice Animals to Euclidean First-Passage Percolation
From Greedy Lattice Animals to Euclidean First-Passage Percolation
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从贪婪的格子动物到欧几里得的第一代渗透
DOI：
10.1007/978-1-4612-2168-5_6
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
C. Newman
中科院分区：
文献类型：
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作者：
C. D. Howard;C. Newman
本文讨论了作者以前提出的欧氏首达渗流模型中有关无限测地线的一些新结果。特别地，对于任意d，概率为1，每个半无限测地线都有一个渐近方向，并且每个方向至少有一个半无限测地线（从每个泊松粒子开始）。这些结果，这还没有被证明为格FPP，不过是基于扩展到欧几里德格FPP的情况下，由于Kesten和亚历山大估计。一个关键的技术成分，我们证明在这里是一个大的偏差估计适用于伯努利渗流贪婪的格子动物。
We discuss some new results concerning infinite geodesics in models of Euclidean First-Passage Percolation (FPP) on ℝdintroduced previously by the authors. In particular, for anyd, with probability one, every semi-infinite geodesic has an asymptotic direction and every direction has at least one semi-infinite geodesic (starting from each Poisson particle). These results, which have not been proved for lattice FPP, are nevertheless based on an extension to the Euclidean case of lattice FPP estimates due to Kesten and Alexander. A key technical ingredient that we prove here is a large deviation estimate for greedy lattice animals applied to Bernoulli percolation.