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Asymptotic distribution of parameters in random maps

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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Submitted on : Monday, October 22, 2018 - 2:50:54 PM
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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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