Two-time distribution functions in the Gaussian model of randomly forced Burgers turbulence

The problem of randomly forced Burgers turbulence (“Burgulence”) is considered in terms of the toy Gaussian Larkin model of directed polymers. In terms of the replica technique the explicit expressions for the two-time four-point free energy distribution function is obtained which makes possible to derive the exact result for the two-time velocity distribution function in the corresponding Burgulence problem.