A Surface View of First-Passage Percolation
A Surface View of First-Passage Percolation
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第一代渗透的表面视图
DOI：
10.1007/978-3-0348-9078-6_94
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
C. Newman
中科院分区：
文献类型：
--
作者：
C. Newman
设\(\tilde B\) (t)为Z d上标准第一次渗流在时间t时从原点到达的位置集，设B0（大致为\(\tilde B\) (t)/t）为其确定性渐近形状。我们将\(\tilde B\) (t)表面的t→∞微观结构与时间最小化路径的生成树及其横向偏差和B0的曲率性质联系起来。最完整的结果被限制为d = 2。
Let \(\tilde B\)(t) be the set of sites reached from the origin by time t in standard first-passage percolation on Z d , and let B0 (roughly lim \(\tilde B\) (t)/t) be its deterministic asymptotic shape. We relate the t → ∞ microstructure of the surface of \(\tilde B\)(t) to spanning trees of time-minimizing paths and their transverse deviations and to curvature properties of B0. The most complete results are restricted to d = 2.