Exact dimension of dynamical stationary measures

2023/03/23 by François Ledrappier, Ledrappier, François, Pablo Lessa +1 · 1 citation
Mathematics · Physics and Astronomy · #28A80 #37A99 #37C45 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2303.13341

openalex publication_date 2023/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a random walk on SL_d(ℝ) with finite first moment and finite entropy. We show that the distributions of the unstable flag space and of the stable flag space are exact dimensional.

Cited by

• Effective Gaps between singular values of non-stationary matrix products subject to non-degenerate noise

Related

• Entropy and dimension of disintegrations of stationary measures
• Exact dimension of Furstenberg measures
• Metric mean dimension, Hölder regularity and Assouad spectrum
• Dimension of Gibbs measures with infinite entropy
• The dimension of the range of a transient random walk