Lingering Random Walks in Random Environment on a Strip
Lingering Random Walks in Random Environment on a Strip
复制标题
带状随机环境中的徘徊随机游走
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
I. Goldsheid
中科院分区：
文献类型：
--
作者：
E. Bolthausen;I. Goldsheid
考虑带上随机环境中的常返随机游动.我们证明，如果RE是i。I. D.并且它的分布不被定义RE的参数空间中的代数次表面支持，则RW表现出（log t）2渐近行为。特殊的代数次表面由一个显式的代数方程组描述，一维有界跳跃行走被视为条带模型的一个特例。如果一维RE是i。I. d.将所述第一和第二组数据进行比较，然后，我们的方法导致一个完整的和建设性的分类可能类型的渐近行为的经常性随机游动。也就是说，RW表现出（log t）2渐近行为，如果RE的分布不支持的参数空间中的超平面，这将被明确描述。如果RE的支撑属于这个超平面，那么相应的RW是一个鞅，并且其渐进行为受中心极限定理的支配。
We consider a recurrent random walk (RW) in random environment (RE) on a strip. We prove that if the RE is i. i. d. and its distribution is not supported by an algebraic subsurface in the space of parameters defining the RE then the RW exhibits the (log t)2 asymptotic behaviour. The exceptional algebraic subsurface is described by an explicit system of algebraic equations.One-dimensional walks with bounded jumps in a RE are treated as a particular case of the strip model. If the one dimensional RE is i. i. d., then our approach leads to a complete and constructive classification of possible types of asymptotic behaviour of recurrent random walks. Namely, the RW exhibits the (log t)2 asymptotic behaviour if the distribution of the RE is not supported by a hyperplane in the space of parameters which shall be explicitly described. And if the support of the RE belongs to this hyperplane then the corresponding RW is a martingale and its asymptotic behaviour is governed by the Central Limit Theorem.