Title: On the Bollobás-Riordan random pairing model of preferential attachment graph
Speaker: Boris Pittel (Ohio State University)
Abstract: The Bollobás-Riordan random pairing model of a preferential attachment graph $G_m^n$ is studied. The degrees of the first $n^{\frac{m}{m+2} - \epsilon}$ vertices are jointly, uniformly asymptotic to an explicit function of the inter-arrival times of a standard Poisson process. Further it is shown that all these vertices have degree $n^{\frac{\epsilon (m+2)}{m}}$ with probability tending to 1 as n goes to infinity. We bound the probability that there exists a pair of large vertex sets with no edges joining them, and use it to identify the ranges of vertex sets that are exponentially unlikely to be isolated, or likely to be vertex-expanding.
