{\rtf1\ansi\ansicpg1252\cocoartf949\cocoasubrtf540 {\fonttbl\f0\fswiss\fcharset0 Helvetica;} {\colortbl;\red255\green255\blue255;} \paperw11900\paperh16840\margl1440\margr1440\vieww9000\viewh8400\viewkind0 \deftab720 \pard\pardeftab720\ql\qnatural \f0\fs24 \cf0 Frank Redig\ \ ``Law of large numbers and large deviations for some random walks\ in dynamic random environment"\ \ We consider a random walk driven by an underlying high-temperature spin-flip\ dynamics. We prove that there exists a unique ergodic measure for the\ environment process if the drift weakly depends on the environment. As a\ consequence, we derive a law of large numbers, central limit theorem and large deviations for the position of the random walk.\ The talk is based on joint work with L. Avena and F. den Hollander\ }