Random walk in random environment and the Kardar-Parisi-Zhang class
Random walk in random environment and the Kardar-Parisi-Zhang class
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Timo Seppalainen, University of Wisconsin
This talk concerns a relationship between two much-studied classes of models Ìýof motion in a random medium, namely Ìýrandom walk in Ìýrandom environment (RWRE) and the Kardar-Parisi-Zhang (KPZ) Ìýuniversality class.Ìý Barraquand and Corwin discovered that in 1+1 dimensional RWRE in a dynamical beta environment the correction to the quenched Ìýlarge deviation principle Ìýobeys KPZ behavior. Ìý In this talk we condition the Ìýbeta walk to escape at an atypical velocity and show that the resulting Doob-transformed RWRE obeys the KPZ wandering exponent 2/3. Ìý The logarithm of the harmonic function in the Doob transform obeys the KPZ 1/3 exponent. Ìý Based on joint work with M\'arton Bal\'azs (Bristol) and Firas Rassoul-Agha (Utah).ÌýÌý