EXPANDING ON AVERAGE DIFFEOMORPHISMS OF SURFACES: EXPONENTIAL MIXING

The paper proves quenched exponential mixing for random C^2 volume-preserving diffeomorphisms on closed surfaces under an expanding-on-average hypothesis, with a polynomial tail µ{C_ω ≥ C} ≤ D1 C^{-1}. The model’s solution mirrors the paper’s structure: finite-time hyperbolicity/tempered times, construction of fake stable manifolds, coupling of standard pairs, a positive-frequency ‘good block’ mechanism leveraging independence, and a tail estimate yielding the C^{-1} bound. Minor differences are expository: the paper develops a finite-time, submartingale-based temperedness and a coupled-recovery scheme with precise tail estimates, while the model sketches these as Kingman–Oseledets/Pliss and “good words with geometric waiting time.” These are compatible perspectives on the same method. The conclusions and key mechanisms agree with the paper’s statements and proofs.