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 transform utilizes a harmonic function defined
by a Busemann-type limit. The Doob-transformed environment is correlated in time, i.i.d. in space, and
under its averaged distribution the transformed walk obeys the wandering exponent 2/3 that agrees with
Kardar-Parisi-Zhang universality. This is a joint work with Marton Balazs and Timo Seppalainen.