# Title: Invariance Principle for the Random Conductance Model in a degenerate ergodic environment

Abstract:In this talk we consider a continuous time random walk $X$ on $\mathbb{Z}^d$ in an environment of random conductances taking values in $[0, \infty)$.  Assuming that the law of the conductances is ergodic with respect to space shifts, we present a quenched invariance principle for $X$ under some moment conditions on the environment. The key result on the sublinearity of the corrector is obtained by Moser's iteration scheme. Under the same conditions we also present a local limit theorem. For the proof some Hölder regularity of the transition density is needed, which follows from a parabolic Harnack inequality. This is joint work with J.-D. Deuschel and M. Slowik. <!--[if !supportLineBreakNewLine]--> <!--[endif]-->

 Location: AHL Lecture Theatre, OMI, Eagle House Speaker(s): SEBASTIAN ANDRES Date: Monday, November 25, 2013 - 15:45 to 16:45