The Rank of Symmetric Matrices

ARITHMETIC COMINATORICS
Topic:The Rank of Symmetric Matrices
Speaker:Kevin Costello
Affiliation:Rutgers, The State University of New Jersey
Date:Tuesday, November 6
Time/Room:2:00pm - 3:00pm/S-101

Let Q(n,p) denote the adjacency matrix of the Erdos-Renyi graph G(n,p), that is to say a symmetric matrix whose entries above the main diagonal are independently set to 1 with probability p and 0 with probability 1-p. We will examine the behavior of the rank of Q(n,p) with an eye on the following questions (whose answer will of course depend on p) 1. What is the probability that Q(n,p) is singular? 2. If Q(n,p) is likely to be singular, can we describe the dependent sets of rows? Joint work with Prof. Van Vu(IAS/Rutgers) and some with Prof. Terence Tao (UCLA)