  Let $\psi(n)\to +0$ and a square-integrable function $f$ be non-zero, then
for the typical mixing automorphism $T$ the set $\{n:\, |(T^nf,f) |>\psi( n)\}$
is infinite. The mildly mixing automorphisms $T$ do not have convergences of
non-zero averages $\frac 1 {k_n} \sum_{i=1}^{k_n}T^if (x)$ with the rate of
$o\left(\frac 1 {k_n}\right)$.
