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.

47 pages, 6 figures. Some proofs were shortened with references to the concurrent paper arXiv:1711.08432

References in corpus (3)

• An almost sure invariance principle for random walks in a space-time random environment
• Kardar-Parisi-Zhang equation and large deviations for random walks in weak random environments
• Exact solution for a random walk in a time-dependent 1D random environment: the point-to-point Beta polymer

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