Sebastian Andres

Berry-Esseen Theorem for the Random Conductance Model

The random conductance model is a well-established model for a random walk in random environment. In recent years the question whether a quenched invariance principle (or quenched functional central limit theorem) holds for such a random walk has been intensively studied, and an invariance principle has meanwhile been established also in the case of general ergodic, degenerate environments satisfying a certain moment condition. In this talk we will present annealed and quenched Berry-Essen theorems, i.e. quantitative central limit theorems, in the case of ergodic degenerate conductances satisfying a strong moment condition and a certain spectral gap estimate. A key ingredient in the proof is an estimate on the variance decay of the semigroup associated with the so-called environment as seen from the particle.
This talk is based on joint work with Stefan Neukamm (TU Dresden).