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

Marton Balazs, Firas Rassoul-Agha, Timo Seppäläinen

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)
190 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)2186-2229
Number of pages47
JournalAnnals of Probability
Issue number4
Early online date4 Jul 2019
Publication statusPublished - Jul 2019


  • Hypergeometric function
  • Beta distribution
  • Doob transform
  • Wandering exponent
  • RWRE
  • Random walk
  • Random environment
  • Large deviations
  • KPZ
  • Kardar-Parisi-Zhang equation


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