Author

Timothée Bénard

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Preprint Sep 2026

Proof of the singularity conjecture for discrete subgroups of $\mathrm{SL}_2(\mathbb{R})$

Let $\mu$ be a finitely supported probability measure on $\mathrm{SL}_2(\mathbb{R})$ whose support generates a Zariski-dense discrete subgroup. We prove that its stationary probability measure on $\mathbb{P}^1(\mathbb{R})$ is singular with respect to the $\mathrm{SO}(2)$-invariant probability measure. The proof compare...

Timothée Bénard · 1 citation