3 papers
math.DS2026
Generic Points on the Staircase and Irregularities in Uniform Distribution
Dmitry Dolgopyat, Omri Sarig
We study the ergodic integrals for linear flows on the infinite staircase, a translation surface with infinite area, and deduce detailed information on the bias properties of local…
math.DS2024
The central limit theorem and rate of mixing for simple random walks on the circle
Klaudiusz Czudek, Dmitry Dolgopyat
We prove the Central Limit Theorem and superpolynomial mixing for environment viewed for the particle process in quasi periodic Diophantine random environment. The main ingredients…
math.PR2021
Local limit theorems for inhomogeneous Markov chains
Dmitry Dolgopyat, Omri Sarig
We prove the Local Limit Theorems for bounded additive functionals of uniformly elliptic inhomogeneous Markov arrays. As an application we obtain the precise asymptotics in the lar…