The circular law for very sparse random matrices

Stochastics Seminar
Thursday, September 13, 2018 - 3:05pm
1 hour (actually 50 minutes)
Skiles 006
School of Mathematics, GaTech

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.