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}
}