On the concentration and the convergence rate with a moment condition in first passage percolation
On the concentration and the convergence rate with a moment condition in first passage percolation
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初代渗流中矩条件下的浓度和收敛速度
DOI：
10.1016/j.spa.2010.03.001
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发表时间：
2008
影响因子：
1.4
通讯作者：
Yu Zhang
中科院分区：
文献类型：
--
作者：
Yu Zhang
我们考虑了第一通道渗流模型的Zdlattice。在这个模型中，我们独立地为每条边e分配一个具有共同分布F的非负通过时间t（e）。设a0，n是从原点到（n，0，.，0）的通过时间。在指数尾假设下，Kesten（1993）[9]和Talagrand（1995）[12]使用不同的方法研究了a0，n的浓度。在此集中度和指数尾假设下，亚历山大（1993）[1]给出了Ea 0，n的收敛速度的估计.本文利用一种特殊的鞅结构，在矩条件下重新研究了a0，n的集中性和收敛速度。
We consider the first passage percolation model on the Zdlattice. In this model, we assign independently to each edge e a non-negative passage time t(e) with a common distribution F. Let a0,nbe the passage time from the origin to (n,0,…,0). Under the exponential tail assumption, Kesten (1993) [9] and Talagrand (1995) [12] investigated the concentration of a0,nfrom its mean using different methods. With this concentration and the exponential tail assumption, Alexander (1993) [1] gave an estimate for the convergence rate for Ea0,n. In this paper, focusing on a moment condition, we reinvestigate the concentration and the convergence rate for a0,nusing a special martingale structure.