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July 2019 Large deviations and wandering exponent for random walk in a dynamic beta environment
Márton Balázs, Firas Rassoul-Agha, Timo Seppäläinen
Ann. Probab. 47(4): 2186-2229 (July 2019). DOI: 10.1214/18-AOP1306

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.

Citation

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Márton Balázs. Firas Rassoul-Agha. Timo Seppäläinen. "Large deviations and wandering exponent for random walk in a dynamic beta environment." Ann. Probab. 47 (4) 2186 - 2229, July 2019. https://doi.org/10.1214/18-AOP1306

Information

Received: 1 February 2018; Published: July 2019
First available in Project Euclid: 4 July 2019

zbMATH: 07114715
MathSciNet: MR3980919
Digital Object Identifier: 10.1214/18-AOP1306

Subjects:
Primary: 60K35, 60K37

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 4 • July 2019
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