Year: 2026
Type: preprint
Abstract: We consider the left translation action of an element $a$ on a finite-volume semisimple homogeneous space $G/Γ$, where $\operatorname{Ad}(a)$ is diagonalizable over $\mathbb{R}$. Assuming exponential mixing, we prove a sub-Gaussian large-deviation estimate for compactly supported smooth test functions. As an application, we prove effective uniqueness of the measure of maximal entropy. We also obtain quantitative pointwise equidistribution for Haar-almost every point on each full expanding horosphere.
Source: arXiv (Cornell University)
Authors: Kim, Taehyeong, Mor, Ron
Institutions: Yale University, Brandeis University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223659174