||Harnack inequalities and local central limit theorem for the polynomial lower tail random conductance model
BOUKHADRA, Omar ,
KUMAGAI, TakashiMATHIEU, Pierre
Journal of the Mathematical Society of Japan
1448 , 2015-10 , Mathematical Society of Japan
We prove upper bounds on the transition probabilities of random walks with i.i.d. random conductances with a polynomial lower tail near 0. We consider both constant and variable speed models. Our estimates are sharp. As a consequence, we derive local central limit theorems, parabolic Harnack inequalities and Gaussian bounds for the heat kernel. Some of the arguments are robust and applicable for random walks on general graphs. Such results are stated under a general setting.