Existence, uniqueness, and canonical description via random limit currents of the measure of maximal fiber entropy for random skew products on compact complex surfaces, with entropy equal to the Furstenberg exponent.
Roda , Classifying Hyperbolic Ergodic Stationary Measures on Compact Complex Surfaces with Large Automorphism Groups, arXiv: 2410.18350
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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.
The paper proves equidistribution of preimages of curves for generic finitely supported random walks of the Cremona group on the inverse limit of spaces of currents across models of the plane.
Existence of dynamical Green functions for random products of non-elementary loxodromic automorphisms of A²_C implies compactly supported μ-stationary measures and stiffness when the action is non-dissipative.
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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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