A probabilistic approach to block sizes in random maps
Probability
2018-12-17 v2 Combinatorics
Abstract
We present a probabilistic approach to the core-size in random maps, which yields straightforward and singularity analysis-free proofs of some results of Banderier, Flajolet, Schaeffer and Soria. The proof also yields convergence in distribution of the rescaled size of the k'th largest 2-connected block in a large random map, for any fixed k > 1, to a Fr\'echet-type extreme order statistic. This seems to be a new result even when k=2.
Keywords
Cite
@article{arxiv.1503.08159,
title = {A probabilistic approach to block sizes in random maps},
author = {Louigi Addario-Berry},
journal= {arXiv preprint arXiv:1503.08159},
year = {2018}
}
Comments
10 pages, 3 figures. To appear in ALEA - Latin American Journal of Probability and Mathematical Statistics