Ph.D. Defense: Suman Chakraborty

The Department of

Statistics and Operations Research

The University of North Carolina at Chapel Hill

Ph.D. Thesis Defense

Public Presentation

Friday, April 6th, 2018

Peabody 010
10:00 AM

Suman Chakraborty

Dense Graph Limits and Applications
(Advisors: Shankar Bhamidi and Andrew Nobel)

We investigate properties of large networks that satisfy certain local conditions. We show that for such networks the number of induced isomorphic copies of subgraphs of size s are approximately same as that of an Erdos-Rényi random graph with appropriate edge connectivity probability as long as s = O(log n). We apply our results to different graph ensembles including exponential random graph models (ERGMs), thresholded graphs from high-dimensional correlation networks, Erdos-Rényi random graphs conditioned on large cliques, random d-regular graphs. We obtain results on site percolation on a class of moderately sparse graphs under some mild limiting assumptions. We will also discuss large networks limits (dense) and other properties of a general class of weighted exponential random graph models