2018/01/31 by Márton Balázs, Firas Rassoul-Agha, Timo Seppäläinen
Mathematics · #math.PR #msc:60K35 #msc:60K37
paper · pdf · doi:10.1214/18-aop1306
published as Ann. Probab. 47(4): 2186-2229 (July 2019) · 47 pages, 6 figures. Some proofs were shortened with references to the concurrent paper arXiv:1711.08432
arxiv created 2018/02/06 · arxiv updated 2021/03/17
Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed environment is correlated in time, i.i.d. in space, and its marginal density function is a product of a beta density and a hypergeometric function. Under its averaged distribution the transformed walk obeys the wandering exponent 2/3 that agrees with Kardar-Parisi-Zhang universality. The harmonic function in the Doob transform comes from a Busemann-type limit and appears as an extremal in a variational problem for the quenched large deviation rate function.