Quenched large deviations for diffusions in a random Gaussian shear flow drift

We prove a full large deviations principle in large time, for a diffusion process with random drift Xt=Wt+∫0tV(Xs) ds, where V is a centered Gaussian shear flow random field independent of the Brownian W. The large deviations principle is established in a “quenched” setting, i.e. is valid almost surely in the randomness of V.