Absolutely continuous Furstenberg measures for finitely-supported random walks

2022/05/23 by Félix Lequen, Lequen, Félix · 1 citation
Mathematics · #22E46 (Primary) #60G50 (Secondary) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2205.11138

openalex publication_date 2022/05/23 · openalex created_date 2022/05/26 · openalex updated_date 2026/07/28

Abstract

In this note, we generalise a Bourgain's construction of finitely-supported symmetric measures whose Furstenberg measure has a smooth density from the case of SL₂(ℝ) to that of a general simple Lie group. The proof is the same as Bourgain's, except that the use of Fourier series is replaced by harmonic analysis on a maximal compact subgroup.

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