Functional central limit theorem for random walks in random environment defined on regular trees
Functional central limit theorem for random walks in random environment defined on regular trees
复制标题
正则树上定义的随机环境中随机游动的函数中心极限定理
DOI：
10.1016/j.spa.2020.02.004
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发表时间：
2020
影响因子：
1.4
通讯作者：
Yuma Uematsu
中科院分区：
文献类型：
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作者：
Andrea Collevecchio;Masato Takei;Yuma Uematsu
摘要研究了定义在b-正则树上的IID随机环境中的随机游动。在环境矩条件下，证明了暂态过程的泛函中心极限定理。我们强调，我们不做一致的椭圆性假设。我们的方法依赖于再生级别，即只访问一次的级别。在此过程中，我们证明了连续再生能级之间的距离有一个几何衰减尾。在本文的第二部分，我们将我们的结果应用于线性边缘增强随机游动，证明了当过程定义在b-正则树上时的FCLT，其中b≥为4，大大改进了第一作者的结果(见Collevecchio(2006年)的定理3)。
Abstract We study Random Walks in an iid Random Environment (RWRE) defined on b-regular trees. We prove a functional central limit theorem (FCLT) for transient processes, under a moment condition on the environment. We emphasize that we make no uniform ellipticity assumptions. Our approach relies on regenerative levels, ie levels that are visited exactly once. On the way, we prove that the distance between consecutive regenerative levels have a geometrically decaying tail. In the second part of this paper, we apply our results to Linearly Edge-Reinforced Random Walk (LERRW) to prove FCLT when the process is defined on b-regular trees, with b≥ 4, substantially improving the results of the first author (see Theorem 3 of Collevecchio (2006)).