Publications in Scientific Journals:
M. Drmota, G. Collet, L. Klausner:
"Limit Laws of Planar Maps with Described Vertex Degrees";
Combinatorics, Probability and Computing,
28
(2019),
4, Special Issue (Analysis and Algorithms);
519
- 541.
English abstract:
We prove a generalmulti-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers D. Our results rely on a classical bijection with mobiles (objects exhibiting a tree structure), combined with refined analytic tools to deal with the systems of equations on infinite variables that arise. We also discuss possible extensions to maps of higher genus and to weighted maps.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1017/S0963548318000573
Created from the Publication Database of the Vienna University of Technology.