## Speaker:

Professor Ofer Zeitouni

## Institution:

University of Minnesota

## Time:

Wednesday, February 28, 2007 - 11:00pm

## Location:

MSTB 107

Abstract: for (transient) one dimensional random walk in random environment, conditions are known that ensure an annealed CLT. One then also have a quenched CLT, with a different (environment dependent) centering.

In higher dimensions, annealed CLT's have been derived in the ballistic case by Sznitman. We prove that in dimension 4 or more, annealed CLT's together with a mild integrability condition imply a quenched CLT. The proof is based on controlling the intersections of two RWRE paths in the same environment.

(joint work with N. Berger)