Takashi Kumagai

We study random walks on Z^d among random conductances {C_{xy}: x,y in Z^d} that permit jumps of arbitrary length. Apart from joint ergodicity with respect to shifts, we assume only that the nearest-neighbor conductances are uniformly positive and...

We consider mixed-type jump processes on metric measure spaces and prove the stability of two-sided heat kernel estimates, heat kernel upper bounds, and parabolic Harnack inequalities. We establish their stable equivalent characterizations in terms...