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PreprintCC BY 4.0arXiv

Large deviations and applications in homogeneous dynamics

  • Taehyeong Kim
  • Ron Mor
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Abstract

We consider the left translation action of an element a on a finite-volume semisimple homogeneous space G/Γ, where Ad(a) is diagonalizable over 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.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026large,
  title = {{Large deviations and applications in homogeneous dynamics}},
  author = {Taehyeong Kim and Ron Mor},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32814},
  eprint = {2610.32814},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32814},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Large deviations and applications in homogeneous dynamics
AU  - Taehyeong Kim
AU  - Ron Mor
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32814
UR  - https://arxiv.org/abs/2610.32814
AB  - We consider the left translation action of an element a on a finite-volume semisimple homogeneous space G/Γ, where Ad(a) is diagonalizable over 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.
ER  -