Large deviations and effective equidistribution

Ilya Khayutin

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We study large deviations for measurable averaging operators on state spaces of dynamical systems. We prove a relatively sharp large deviation result in terms of the norm gap of the averaging operator. Developing ideas of Linnik and Ellenberg, Michel, and Venkatesh, we deduce an effective equidistribution theorem. The novelty of our results is that they apply to measures with suboptimal bounds on the mass of Bowen balls. We present two new applications of our results. The first one is effective rigidity for the measure of maximal entropy on S-arithmetic quotients. This is a partial extension of a recent result of Rühr. The second one is non-escape of mass for measures having large entropy in a non-Archimedean place. This generalizes known results for real flows.

Original languageEnglish (US)
Pages (from-to)3050-3106
Number of pages57
JournalInternational Mathematics Research Notices
Issue number10
StatePublished - May 1 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics


Dive into the research topics of 'Large deviations and effective equidistribution'. Together they form a unique fingerprint.

Cite this