Martin Slowik

Invariance principle for the random conductance model in a degenerate ergodic environment

We study a continuous time random walk, X, on Zd in an environment of random conductances taking values in (0,∞). We assume that the law of the conductances is ergodic with respect to space shifts. We prove a quenched invariance principle for X under some moment conditions of the environment. The key result on the sublinearity of the corrector is obtained by Moser’s iteration scheme.

Harnack inequalities on weighted graphs and some applications to the random conductance model

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

Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights

X

Heat kernel estimates for random walks with degenerate weights

X in an environment of ergodic random conductances taking values in

Invariance Principle for the one-dimensional dynamic Random Conductance Model under Moment Conditions

(0, \infty )

Green kernel asymptotics for two-dimensional random walks under random conductances.

(0,∞) satisfying some moment conditions.