Asymptotic evolution of acyclic random mappings

Steven N. Evans, Tye Lidman

An acyclic mapping from an $n$ element set into itself is a mapping $\varphi$ such that if ${\varphi }^k(x)=x$ for some $k$ and $x$, then $\varphi (x)=x$. Equivalently, ${\varphi }^{\ell }={\varphi }^{\ell +1}=...$ f…