Geodesic
Generic correlations and ergodic averages for strongly and mildly mixing automorphisms
Matematičeskie zametki, Tome 116 (2024) no. 3, pp. 438-444 Cet article a éte moissonné depuis la source Math-Net.Ru

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Given a sequence $\psi(n)\to +0$ and a square integrable nonzero function $f$, the set $\{n:|(T^nf,f)|>\psi(n)\}$ is infinite for any generic mixing automorphism $T$. For mildly mixing automorphisms $T$, the nonzero averages $1/{k_n}\sum_{i=1}^{k_n}T^if (x)$ do not converge at a rate of $o(1/{k_n})$.
Keywords: decay of correlations, ergodic average, generic mixing automorphism, partial mixing, mild mixing, partial rigidity. 
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V. V. Ryzhikov. Generic correlations and ergodic averages for strongly and mildly mixing automorphisms. Matematičeskie zametki, Tome 116 (2024) no. 3, pp. 438-444. http://geodesic.mathdoc.fr/item/MZM_2024_116_3_a8/

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