Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 10 novembre 2020 à 15h00 en visioconférence, Hosam Mahmoud nous parlera de : Pólya urns and Apollonian network (delayed by a few minutes, eg 15h15, stay tuned)

Résumé : We briefly review a number of random networks in recent areas of interest of the speaker, and discuss the issues that arise. We present the Apollonian network as a case study. We study the distribution of the degrees of vertices as they age in the evolutionary process. Asymptotically, the (suitably-scaled) degree of a node with a fixed label has a Mittag-Leffler-like limit distribution. The degrees of nodes of later ages have different asymptotic distributions, influenced by the time of their appearance. The very late arrivals have a degenerate distribution. The result is obtained via triangular Pólya urns. Also, via the Bagchi-Pal urn, we show that the number of terminal nodes asymptotically follows a Gaussian law. We prove that the total weight of the network asymptotically follows a Gaussian law, obtained via martingale methods. Similar results carry over to the sister structure of the k-trees.

[NB: For this talk, we have the pleasure to join the "Applied Mathematics Webinar", Jeddah - Riadh - Dammam - Tunis]

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