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H\"older regularity of stationary measures

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arxiv 2209.12342 v1 pith:DH7SXQB4 submitted 2022-09-25 math.DS math.PR

Anton Gorodetski , Victor Kleptsyn , Grigorii Monakov This is my paper · ORCID
classification math.DSmath.PR
keywords olderstationarymeasuresrandomclassicalconditionsconsidercontinuity
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We consider smooth random dynamical systems defined by a distribution with a finite moment of the norm of the differential, and prove that under suitable non-degeneracy conditions any stationary measure must be H\"older continuous. The result is a vast generalization of the classical statement on H\"older continuity of stationary measures of random walks on linear groups.

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  1. $L^2$-Flattening of Self-similar Measures on Non-degenerate Curves

    math.CA 2025-07 conditional novelty 8.0 of 10

    Self-similar measures pushed to non-degenerate curves satisfy optimal L^p-flattening estimates for their Fourier transforms, implying quantitative dimension improvement under convolution.

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