Generic Correlations and Ergodic Averages for Strongly and Mildly Mixing Automorphisms

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 \(o(1/{k_n})\) .