STATISTICS COLLOQUIUM
Panpan Zhang
Visiting Assistant Professor
University of Connecticut
Joint distribution of nodes of different outdegrees and the degree profile in preferential dynamic attachment circuits
ABSTRACT
We investigate the joint distribution of nodes of different outdegrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the asymptotic distribution of the number of the nodes of outdegree 0 (terminal nodes) and outdegree 1 in a very large circuit. The expectation and variance of the number of those two types of nodes are both linear with respect to the age of the circuit. We show that the number of nodes of outdegree 0 and 1 asymptotically follows a bivariate normal distribution via martingale methods. We also study the exact distribution of the degree of a node as the circuit ages via a series of Pólya-Eggenberger urn models with “hiccups” in between. The exact expectation and variance of the degree of nodes are determined by recurrence methods. Phase transitions of these degrees are discussed briefly. This is a joint work with Hosam M. Mahmoud.
DATE: Wednesday, September 14, 2016
TIME: 4:00 pm – 5:00 pm
PLACE: Philip E. Austin Bldg., Rm. 105
Coffee will be served at 3:30 in the Noether Lounge (AUST 326)
For more information, contact: Tracy Burke at tracy.burke@uconn.edu