The Annals of Probability

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

Márton Balázs, Firas Rassoul-Agha, and Timo Seppäläinen

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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
Received: February 2018
First available in Project Euclid: 4 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.aop/1562205707

Digital Object Identifier
doi:10.1214/18-AOP1306

Mathematical Reviews number (MathSciNet)
MR3980919

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K37: Processes in random environments

Keywords
Beta distribution Doob transform hypergeometric function Kardar–Parisi–Zhang KPZ large deviations random environment random walk RWRE wandering exponent

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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