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

Xinxing Chen

Stochastic Processes and their Applications, 2016, vol. 126, issue 10, 3041-3064

Abstract: We consider a weighted lattice Zd with conductance μe=∣e∣−α. 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 α∈(−1,0), two independent random walks on such weighted lattice will collide infinitely many times while they are transient.

Keywords: Random walks; Heat kernel; Gaussian bound; Collisions; Intrinsic metric (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:10:p:3041-3064

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DOI: 10.1016/j.spa.2016.03.011

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