Speaker: Jian Wang

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

Abstract: We establish the quenched local limit theorem for reversible random walk on $\Z^d$ (with $d\ge 2$) 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. This is based on a joint work with Xin Chen and Takashi Kumagai.