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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 Doobtransformed 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 KardarParisiZhang universality. The harmonic function in the Doob transform comes from a Busemanntype limit and appears as an extremal in a variational problem for the quenched large deviation rate function.
Original language  English 

Pages (fromto)  21862229 
Number of pages  47 
Journal  Annals of Probability 
Volume  47 
Issue number  4 
Early online date  4 Jul 2019 
DOIs  
Publication status  Published  Jul 2019 
Keywords
 Hypergeometric function
 Beta distribution
 Doob transform
 Wandering exponent
 RWRE
 Random walk
 Random environment
 Large deviations
 KPZ
 KardarParisiZhang equation
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Dive into the research topics of 'Large deviations and wandering exponent for random walk in a dynamic beta environment'. Together they form a unique fingerprint.Projects
 1 Active

Stochastic interacting systems: connections, fluctuations and applications
1/06/18 → 19/02/22
Project: Research
Profiles

Dr Marton Balazs
 School of Mathematics  Reader in Probability
 Probability, Analysis and Dynamics
 Probability
Person: Academic , Member