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Asymptotic Distribution of Parameters in Random Maps Bodini, Olivier Courtiel, Julien Dovgal, Sergey Hwang, Hsien-Kuei Random maps Analytic combinatorics Rooted Maps Beta law Limit laws Patterns Generating functions Riccati equation We consider random rooted maps without regard to their genus, with fixed large number of edges, and address the problem of limiting distributions for six different parameters: vertices, leaves, loops, root edges, root isthmus, and root vertex degree. Each of these leads to a different limiting distribution, varying from (discrete) geometric and Poisson distributions to different continuous ones: Beta, normal, uniform, and an unusual distribution whose moments are characterised by a recursive triangular array. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Olivier Bodini and Julien Courtiel and Sergey Dovgal and Hsien-Kuei Hwang 2018 Is Part Of LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AofA.2018.13 urn:nbn:de:0030-drops-89069 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.13 eng https://creativecommons.org/licenses/by/3.0/legalcode