Transient Random Walks on 2D-Oriented Lattices
Transient Random Walks on 2D-Oriented Lattices
复制标题
二维晶格上的瞬态随机游走
DOI：
10.1137/s0040585x97983353
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发表时间：
2006
影响因子：
0.6
通讯作者：
A. Ny
中科院分区：
文献类型：
--
作者：
N. Guillotin;A. Ny
我们研究了Z2定向型上简单随机游动的渐近行为。所考虑的晶格不是在垂直轴上定向的，而是在水平轴上单向的，其随机取向的分布是由一个动力学系统产生的。我们给出了简单随机游动在几乎每一个这样的定向格上暂态的生成光滑性的一个充分条件，作为说明，我们给出了方向的非齐次分布或相关分布的一大类例子。对于遍历动力系统，我们还证明了一个强大数定律，并且，在I.I.D.的特殊情况下，证明了一个强大数定律。利用非常规的归一化方法，我们解决了一个公开问题，证明了函数在空间D([0；1[；R2)中的函数极限定理。
We study the asymptotic behavior of the simple random walk on oriented versions ofZ 2 . The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose distributions are generated by a dynamical system. We flnd a su‐cient condition on the smoothness of the generation for the transience of the simple random walk on almost every such oriented lattices, and as an illustration we provide a wide class of examples of inhomogeneous or correlated distributions of the orientations. For ergodic dynamical systems, we also prove a strong law of large numbers and, in the particular case of i.i.d. orientations, we solve an open problem and prove a functional limit theorem in the space D([0;1[;R 2 ) of cµadlµag functions, with an unconventional normalization.