A special feature of Probability and Statistics Day at UMBC 2015 is that the conference, including the workshop, is open to all statistics graduate students
from UMBC and local universites free of charge; however, REGISTRATION IS REQUIRED! The deadline to register is Friday,
April 3, 2015. // REGISTER NOW
For more information, contact any member of the organizing committee:
Bimal Sinha
Conference Chair
443.538.3012
Kofi Adragni
410.455.2406
Yvonne Huang
410.455.2422
Yaakov Malinovsky
410.455.2968
Thomas Mathew
410.455.2418
Nagaraj Neerchal
410.455.2437
DoHwan Park
410.455.2408
Junyong Park
410.455.2407
Anindya Roy
410.455.2435
Elizabeth Stanwyck
410.455.5731
Participant Information
Panpan Zhang
Paper: The degree profile and weight in Apollonian networks and k-trees
We investigate the degree profile and total weight in Apollonian networks. 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 (timestamp) has a Mittag-Leffler-like limit distribution. The degree of nodes with intermediate age (growing, but not too fast, label) have different asymptotic distributions, influenced by their labels. The very late arrivals have a degenerate distribution. The result is obtained via triangular Polya 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, with minor modification in the proof methods, done mutatis mutandis.
