Gaussian bounds and collisions of variable speed random walks on lattices with power law conductances

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Chen, Xinxing¹ 

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

关键词: Random walks;    Heat kernel;    Gaussian bound;    Collisions;    Intrinsic metric;   

DOI  :  10.1016/j.spa.2016.03.011

来源: Elsevier

【 摘 要 】

We consider a weighted lattice Z(d) with conductance mu(e) =vertical bar e vertical bar(-alpha). We show that the heat kernel of a variable speed random walk on it satisfies a two-sided Gaussian bound by using an intrinsic metric. We also show that when d = 2 and alpha is an element of (-1, 0), two independent random walks on such weighted lattice will collide infinitely many times while they are transient. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free