## The Annals of Probability

### Large deviations and wandering exponent for random walk in a dynamic beta environment

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 47, Number 4 (2019), 2186-2229.

Dates
First available in Project Euclid: 4 July 2019

https://projecteuclid.org/euclid.aop/1562205707

Digital Object Identifier
doi:10.1214/18-AOP1306

Mathematical Reviews number (MathSciNet)
MR3980919

Zentralblatt MATH identifier
07114715

#### Citation

Balázs, Márton; Rassoul-Agha, Firas; Seppäläinen, Timo. Large deviations and wandering exponent for random walk in a dynamic beta environment. Ann. Probab. 47 (2019), no. 4, 2186--2229. doi:10.1214/18-AOP1306. https://projecteuclid.org/euclid.aop/1562205707

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