Precise asymptotics of longest cycles in random permutations without macroscopic cycles

Volker Betz, Julian Mühlbauer, Helge Schäfer +1

We consider Ewens random permutations of length $n$ conditioned to have no cycle longer than $n^{\beta }$ with $0<\beta <1$ and to study the asymptotic behaviour as $n\to \infty$. We obtain ver…