Asymptotic distribution of parameters in random maps

Distribution asymptotique de paramètres dans des cartes aléatoires

Olivier Bodini (1) , Julien Courtiel (2, 3) , Sergey Dovgal , Hsien-Kuei Hwang (4)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 Equipe AMACC - Laboratoire GREYC - UMR6072
3 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
4 STAT Sinica - Institute of Statistical Science

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.

Domaines: Combinatoire [math.CO]

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⟩