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

Abstract

We consider a weighted lattice $Z^d$ with conductance ${\mu }_e=|e{|}^{-\alpha }$. 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 $\alpha \in (-1,0)$, two independent random walks on such weighted lattice will collide infinite many times while they are transient.

References in corpus (1)

• Pointwise upper estimates for transition probability of continuous time random walks on graphs