Timo Seppäläinen (1) Random walk in random environment and the Kardar-Parisi-Zhang class, part 1
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 11/07/2017

This talk describes 1+1 dimensional directed random walks in correlated random environments that obey the Kardar-Parisi-Zhang 2/3 fluctuation exponent. This is in marked contrast with the IID environment case where the walk satisfies a quenched central limit theorem with the standard diffusive scaling. We discuss walks in correlated environments that arise from two sources: (i) from limits of quenched polymer measures when the length of the polymer path is taken to infinity, and (ii) from limits of RWRE in an IID environment conditioned on an atypical velocity. In both cases results currently exist only for exactly solvable models. In case (i) the exactly solvable case is the log-gamma polymer. In case (ii) the exactly solvable model is the RWRE in an IID beta environment, whose exact solvability was discovered by Barraquand and Corwin. This talk is based on joint papers with Marton Balazs (University of Bristol), Nicos Georgiou (University of Sussex), Firas Rassoul-Agha (University of Utah), and Atilla Yilmaz (Koc University).
Presented at the 27th Annual PCMI Summer Session, Random Matrices, held June 25 – July 15, 2017. The residential, three-week Summer Session is the flagship activity of the IAS/Park City Mathematics Institute (PCMI).

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