Geodesic
Generic correlations and ergodic averages for strongly and mildly mixing automorphisms
Matematičeskie zametki, Tome 116 (2024) no. 3, pp. 438-444

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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. 
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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