Hölder regularity of stationary measures

2022/09/25 by Anton Gorodetski, Victor Kleptsyn, Gorodetski, Anton +3 · 2 citations
Computer Science · Mathematics · #37H05 #60B20 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2209.12342

openalex publication_date 2022/09/25 · openalex created_date 2022/12/31 · openalex updated_date 2026/07/28

Abstract

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 Hölder continuous. The result is a vast generalization of the classical statement on Hölder continuity of stationary measures of random walks on linear groups.

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• Localization of the 1D Non-Stationary Anderson Model
• L²-Flattening of Self-similar Measures on Non-degenerate Curves

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