Under compact support, gap, pinching, and weak-* proximity to volume-preservation, random walks by C² diffeomorphisms on a closed manifold M admit a unique atom-free stationary measure Υ_μ of full Frostman dimension to which μ^{*n} * δ_x converges for most x.
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Rigidity and equidistribution of random walks by diffeomorphisms near the conservative regime
Under compact support, gap, pinching, and weak-* proximity to volume-preservation, random walks by C² diffeomorphisms on a closed manifold M admit a unique atom-free stationary measure Υ_μ of full Frostman dimension to which μ^{*n} * δ_x converges for most x.