## Stability and instability of Gaussian heat kernel estimates for random walks among time-dependent conductances.(English)Zbl 1338.60196

Summary: We consider time-dependent random walks among time-dependent conductances. For discrete time random walks, we show that, unlike the time-independent case, two-sided Gaussian heat kernel estimates are not stable under perturbations. This is proved by giving an example of a ballistic and transient time-dependent random walk on $$\mathbb{Z}$$ among uniformly elliptic time-dependent conductances. For continuous time random walks, we show the instability when the holding times are i.i.d. $$\exp(1)$$, and in contrast, we prove the stability when the holding times change by sites in such a way that the base measure is a uniform measure.

### MSC:

 60J35 Transition functions, generators and resolvents 60J05 Discrete-time Markov processes on general state spaces 60J25 Continuous-time Markov processes on general state spaces 60J45 Probabilistic potential theory
Full Text: