Dmitry Dolgopyat, Changguang Dong, Adam Kanigowski, Peter Nándori
Published 2020-04-15Version 1
We study mixing properties of generalized $T, T^{-1}$ transformation. We discuss two mixing mechanisms. In the case the fiber dynamics is mixing, it is sufficient that the driving cocycle is small with small probability. In the case the fiber dynamics is only assumed to be ergodic, one needs to use the shearing properties of the cocycle. Applications include the Central Limit Theorem for sufficiently fast mixing systems and the estimates on deviations of ergodic averages.
Central limit theorem for commutative semigroups of toral endomorphisms
Central Limit theorem and cohomological equation on homogeneous space
Central limit theorem and stable laws for intermittent maps
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