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Conference Papers Year : 2018

Asymptotic distribution of parameters in random maps

Distribution asymptotique de paramètres dans des cartes aléatoires

Abstract

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.
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Dates and versions

hal-01900814 , version 1 (22-10-2018)

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Olivier Bodini, Julien Courtiel, Sergey Dovgal, Hsien-Kuei Hwang. Asymptotic distribution of parameters in random maps. 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), Jun 2018, Uppsala, Sweden. pp.13:1-13:12, ⟨10.4230/LIPIcs.AofA.2018.13⟩. ⟨hal-01900814⟩
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