Limit laws of planar maps with prescribed vertex degrees. (4th February 2019)

• Record Type: Journal Article
• Authors: Collet, G.; Drmota, M.; Klausner, L. D.
• Is Part Of: Combinatorics, probability and computing. Volume 28:Number 4(2019)
• Page Start: 519
• Page End: 541
• Publication Date: 2019-02-04
• Subjects: Primary 05A16, -- Secondary 05C07, -- 05C10, -- 05C30; Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548318000573
• Languages: English
• ISSNs: 0963-5483

Abstract

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.