Sebastian Andres, Jean-Dominique Deuschel and Martin Slowik Harnack inequalities on weighted graphs and some applications to the random conductance model Probab. Theory Relat. Fields: 1-47 2015 http://dx.doi.org/10.1007/s00440-015-0623-y
Abstract: We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk X in an environment of ergodic random conductances taking values in (0,∞) satisfying some moment conditions.
Sebastian Andres, Jean-Dominique Deuschel and Martin Slowik Invariance principle for the random conductance model in a degenerate ergodic environment Ann. Probab., 43(4): 1866-1891 2015 http://dx.doi.org/10.1214/14-AOP921
2014
Sebastian Andres, Jean-Dominique Deuschel and Martin Slowik Heat kernel estimates for random walks with degenerate weights 2014 http://arxiv.org/abs/1412.4338