Large deviations for the chemical distance in supercritical Bernoulli percolation
Large deviations for the chemical distance in supercritical Bernoulli percolation
复制标题
超临界伯努利渗滤中化学距离偏差较大
DOI：
10.1214/009117906000000881
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发表时间：
2004
影响因子：
2.3
通讯作者：
R. Marchand
中科院分区：
文献类型：
--
作者：
Olivier Garet;R. Marchand
化学距离D（x，y）是无限伯努利渗流簇中两点x和y之间的最短开放路径的长度。本文研究了这一随机度量的渐近行为，证明了对于依赖于维数和渗流参数的适当范数μ，事件{0 Particix，D（0，x）/μ（x）<$（1-e，1+e）}的概率在<$x <$1趋于无穷大时呈指数下降.从这个界，我们还得到了相应的渐近形状结果的大偏差不等式。
The chemical distance D(x, y) is the length of the shortest open path between two points x and y in an infinite Bernoulli percolation cluster. In this work, we study the asymptotic behavior of this random metric, and we prove that, for an appropriate norm μ depending on the dimension and the percolation parameter, the probability of the event {0↔x, D(0,x)/μ(x) ∉ (1-e,1+e)} exponentially decreases when ∥x∥ 1 tends to infinity. From this bound we also derive a large deviation inequality for the corresponding asymptotic shape result.