English

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

Probability 2016-08-31 v2

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.

Keywords

Cite

@article{arxiv.1605.08383,
  title  = {The number of cycles in random permutations without long cycles is asymptotically Gaussian},
  author = {Volker Betz and Helge Schäfer},
  journal= {arXiv preprint arXiv:1605.08383},
  year   = {2016}
}