CS 789 THEORY SEMINAR [home]

Speaker:  Rick Durrett
Affiliation: Mathematics, Cornell University
Date: Monday, January 20, 2003
Title: Rigorous Results for the Calloway-Hopcroft-
        Kleinberg-Newman-Strogatz Random Graph

Abstract:

The five authors mentioned in the title introduced and studied a model of a growing network in which at each time a new vertex and a number of new edges with mean delta are added. In the case in which the number of edges added has a Poisson distribution, this is equivalent to a no homogeneous random graph model that is closely related to a model studied by Durrett, Kesten and Zhang a dozen years ago. Using some old and some new ideas we will show that the critical value delta_c is 1/8 and give results for the power law decay of cluster sizes in the critical and subcritical regimes.