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arXiv · 2205.11138

Absolutely continuous Furstenberg measures for finitely-supported random walks

Félix Lequen
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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 $\mathrm{SL}_2(\mathbb{R})$ 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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Félix Lequen. 2022-05-23. Absolutely continuous Furstenberg measures for finitely-supported random walks. https://arxiv.org/abs/2205.11138

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