一类 i.i.d. 环境中的弹道随机游动的淬灭不变原理
概率论
2008-01-05 v3
摘要
我们证明，在维数大于等于 2 的 i.i.d. 环境中的每个随机游动，若其在某一方向上几乎必然具有正速度、满足退火不变原理以及对再生时间的一些温和可积条件，则也满足淬灭不变原理。该论证基于交集估计以及 Bolthausen 和 Sznitman 的一个定理。
引用
@article{arxiv.math/0702306,
title = {A quenched invariance principle for certain ballistic random walks in i.i.d. environments},
author = {Noam Berger and Ofer Zeitouni},
journal= {arXiv preprint arXiv:math/0702306},
year = {2008}
}
备注
This version includes an extension of the results to cover also dimensions 2,3, and also corrects several minor innacuracies. The previous version included a correction of a minor error in (3.21) (used for d=4); The correction pushed the assumption on moments of regeneration times to >8