Year: 2026
Type: preprint
Abstract: Let $μ$ 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 compares winding variances on finite covers of a closed hyperbolic surface and uses a topological obstruction.
Source: arXiv (Cornell University)
Author: Bénard, Timothée
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213432540