Probability Seminar: Suman Chakraborty

Suman Chakraborty
University of North Carolina-Chapel Hill

Pseudo-random graphs and applications

We consider classes of pseudo-random graphs on n vertices for which the degree of every vertex and the co-degree between every pair of vertices are in the intervals (np-Cn^δ,np+Cn^δ) and (np^2-Cn^δ,np^2+Cn^δ) respectively, for some absolute constant C, and p,δ∈(0,1). We show that for such pseudo-random graphs the number of induced isomorphic copies of subgraphs of size s are approximately same as that of an Erdos-Renyi random graph with edge connectivity probability p as long as s=O(logn), when p∈(0,1/2]. When p∈(1/2,1) we obtain a similar result. We apply our results to different graph ensemble including exponential random graph models (ERGMs), thresholded graphs from high-dimensional correlation networks, Erdos-Renyi random graphs conditioned on large cliques, random d-regular graphs and graphs obtained from vector spaces over binary fields. If time permits, we will discuss dense graph limits of some exponential models of weighted networks.

Refreshments will be served at 3:45 in the 3rd floor lounge of Hanes Hall