We study random dynamical systems generated by smooth surface diffeomorphisms. Brown and Rodriguez Hertz showed that hyperbolic stationary measures typically have the SRB property—meaning absolute continuity along unstable manifolds—except in the presence of specific obstructions. We aim to identify conditions under which SRB stationary measures are absolutely continuous with respect to Lebesgue measure on the ambient space.

This is a joint work with Aaron Brown, Homin Lee, and Yuping Ruan.