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

Volker Betz; Helge Schäfer

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arXiv · 1605.08383

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

Volker Betz·Helge Schäfer

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Abstract

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 asymptotic behavior of the set of allowed cycle lengths, we derive asymptotic expansions for the corresponding expected value and variance.

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Volker Betz, Helge Schäfer. 2016-05-26. The number of cycles in random permutations without long cycles is asymptotically Gaussian. https://arxiv.org/abs/1605.08383

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