A HSU–ROBBINS–ERDŐS STRONG LAW IN FIRST-PASSAGE PERCOLATION BY DANIEL AHLBERG
A HSU–ROBBINS–ERDŐS STRONG LAW IN FIRST-PASSAGE PERCOLATION BY DANIEL AHLBERG
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丹尼尔·阿尔伯格 (DANIEL AHLBERG) 的《第一通道渗透中的 HSU-Robbins-ERDŐS 强有力法则》
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Li Xiu
中科院分区：
文献类型：
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作者：
Feng Xiaoli;Zhang Hongtu;Sun Yun;Li Xiu
首次通过渗流背景下的大偏差最早由Grimmett和Kesten在20世纪80年代初研究，此后在各种研究中重新研究。然而，这些研究都没有提供一个精确的多项式阶矩的存在性和概率尾部的衰减之间的关系。本文导出了这样一个关系式，并用它来加强形定理的结论。相反，它的一维对应的Hsu-Robbins-Erdés强定律，这种加强是在没有施加高阶矩条件。
Large deviations in the context of first-passage percolation was first studied in the early 1980s by Grimmett and Kesten, and has since been revisited in a variety of studies. However, none of these studies provides a precise relation between the existence of moments of polynomial order and the decay of probability tails. Such a relation is derived in this paper, and is used to strengthen the conclusion of the shape theorem. In contrast to its one-dimensional counterpart—the Hsu–Robbins–Erdős strong law—this strengthening is obtained without imposing a higher-order moment condition.