Slow convergences of ergodic averages

Valery V. Ryzhikov

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arXiv · 2211.06599

Slow convergences of ergodic averages

Valery V. Ryzhikov

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Abstract

Birkhoff's theorem states that for an ergodic automorphism, the time averages converge to the space average. Given sequence $\psi(n)\to+0$, U. Krengel proved that for any ergodic automorphism there is an indicator such that the corresponding time averages converged a.e. with a rate slower than $\psi$. We prove again similar statements answering a question of I. Podvigin in passing.

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Valery V. Ryzhikov. 2022-11-12. Slow convergences of ergodic averages. https://arxiv.org/abs/2211.06599

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