The circular law for very sparse random matrices

Series: 
Stochastics Seminar
Thursday, September 13, 2018 - 3:05pm
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
School of Mathematics, GaTech
Organizer: 
Let (A_n) be a sequence of random matrices, such that for every n, A_n is n by n with i.i.d. entries, and each entry is of the form b*x, where b is a Bernoulli random variable with probability of success p_n, and x is an independent random variable of unit variance. We show that, as long as n*p_n converges to infinity, the appropriately rescaled spectral distribution of A_n converges to the uniform measure on the unit disc of complex plane. Based on joint work with Mark Rudelson.