Pattern occurrences in random planar maps
Combinatorics
2019-05-20 v2 Probability
Abstract
We consider planar maps adjusted with a (regular critical) Boltzmann distribution and show that the expected number of pattern occurrences of a given map is asymptotically linear when the number n of edges goes to infinity. The main ingredient for the proof is an extension of a formula by Liskovets (1999).
Cite
@article{arxiv.1801.10007,
title = {Pattern occurrences in random planar maps},
author = {Michael Drmota and Benedikt Stufler},
journal= {arXiv preprint arXiv:1801.10007},
year = {2019}
}