Random walk in random scenery and self-intersection local times in dimensions d ≥ 5
Random walk in random scenery and self-intersection local times in dimensions d ≥ 5
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DOI：
10.1007/s00440-006-0014-5
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发表时间：
2007-02
影响因子：
2
通讯作者：
A. Asselah;F. Castell
中科院分区：
文献类型：
--
作者：
A. Asselah;F. Castell
设{Sk，k≥0}为上的对称随机漫步，是一个有尾衰的有中心的i.d随机变量的独立随机场。我们考虑随机场景中的随机漫步。对于β > 1/2和α > 1，我们给出了概率{Xn>nβ}的渐近性。为了得到这样的渐近性，我们建立了自交局部时间过程的大偏差估计，其中(x)是站点到时间的访问次数。
Let {Sk,k≥ 0} be a symmetric random walk on, andan independent random field of centered i.i.d. random variables with tail decay. We consider a random walk in random scenery, that is. We present asymptotics for the probability, over both randomness, that {Xn>nβ} for β > 1/2 and α > 1. To obtain such asymptotics, we establish large deviations estimates for the self-intersection local times process, whereln(x) is the number of visits of sitexup to timen.