Quenched local limit theorem for random conductance models with long-range jumps

2024/02/11 by Chen, Xin, Kumagai, Takashi, Wang, Jian
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2402.07212

Abstract

We establish the quenched local limit theorem for reversible random walk on \Z^d (with d≥ 2) among stationary ergodic random conductances that permit jumps of arbitrary length. The proof is based on the weak parabolic Harnack inequalities and on-diagonal heat-kernel estimates for long-range random walks on general ergodic environments. In particular, this partly solves \cite[Open Problem 2.7]BCKW, where the quenched invariance principle was obtained. As a byproduct, we prove the maximal inequality with an extra tail term for long-range reversible random walks, which in turn yields the everywhere sublinear property for the associated corrector.

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