A probabilistic approach to block sizes in random maps

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 Fréchet-type extreme order statistic. This seems to be a new result even when k=2.

arXiv comment10 pages, 3 figures. To appear in ALEA - Latin American Journal of Probability and Mathematical Statistics