Helge Schäfer

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math.PR2017

Random permutations without macroscopic cycles

Volker Betz, Helge Schäfer, Dirk Zeindler

We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^{β}$ with $0 < β < 1$ , in the limit of large $n$ . Since in unconstrained uniform random…

math.PR2016

The number of cycles in random permutations without long cycles is asymptotically Gaussian

Volker Betz, Helge Schäfer

For uniform random permutations conditioned to have no long cycles, we prove that the total number of cycles satisfies a central limit theorem. Under additional assumptions on the…