A case of the limit distribution of the number of cyclic vertices in a random mapping

We consider the number of cyclic vertices in a random single-valued mapping of a set of size $n$ whose graph contains $m$ cycles. We obtain a theorem that describes the limit behaviour of this characteristic as $n\to\infty$, $m/\ln n\to\infty$, $m/\ln n=O(\ln n)$.
This research was supported by grant 1758.2003.1 of the President of Russian Federation for support of the leading scientific schools.