Quenched local central limit theorem for random walks in a time-dependent balanced random environment

Abstract

We prove a quenched local central limit theorem for continuous-time random walks in ${\mathbb{Z}}^d,d\ge 2$, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian upper and lower bounds for quenched and (positive and negative) moment estimates of the transition probabilities and asymptotics of the discrete Green function.

arXiv comment42 pages, 3 figures. Results and their proofs in the previous version are modified and improved