Exit laws from large balls of (an)isotropic random walks in random environment
Exit laws from large balls of (an)isotropic random walks in random environment
复制标题
随机环境中（非）各向同性随机游走大球的退出定律
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
E. Bolthausen
中科院分区：
文献类型：
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作者：
Erich Baur;E. Bolthausen
研究了独立同分布中随机游动在Zd（d≥3）中大球的退出律.随机环境，是对应于简单随机游走的环境的小扰动。在一个中心条件下的措施管理的环境中，我们证明了出口法律是接近的对称随机游走，我们确定为扰动的简单随机游走。我们得到的总变化距离的界限，以及本地的结果比较边界段上的退出概率。作为应用，我们证明了随机环境中随机游动的瞬时性。
我们的工作包括Bolthausen和Zeitouni [Probab.理论相关领域138（2007）581-645]。由于Bolthausen和Zeitouni（2007）中的几个证明是不完整的，因此第一作者的论文[Long-time behavior of random walks in random environment（2013）苏黎世大学]中给出了一种稍微不同的方法。在这里，我们将这种方法扩展到某些各向异性的行走，并提供了一个完全微扰理论的随机环境中的随机行走进一步。
We study exit laws from large balls in Zd, d≥3, of random walks in an i.i.d. random environment that is a small perturbation of the environment corresponding to simple random walk. Under a centering condition on the measure governing the environment, we prove that the exit laws are close to those of a symmetric random walk, which we identify as a perturbed simple random walk. We obtain bounds on total variation distances as well as local results comparing exit probabilities on boundary segments. As an application, we prove transience of the random walks in random environment.
Our work includes the results on isotropic random walks in random environment of Bolthausen and Zeitouni [Probab. Theory Related Fields 138 (2007) 581–645]. Since several proofs in Bolthausen and Zeitouni (2007) were incomplete, a somewhat different approach was given in the first author’s thesis [Long-time behavior of random walks in random environment (2013) Zurich Univ.]. Here, we extend this approach to certain anisotropic walks and provide a further step towards a fully perturbative theory of random walks in random environment.