Bounding the least singular value of random sign matrices

Nathan Tung
Fri, Jan 19 2024, 4:00pm

Abstract: We will use the random sign matrix model to examine methods for bounding the probability that the least singular value is small. This quantity is relevant in many (and in some cases the only known) methods to establish limiting spectral laws of all sorts of random matrix models. It's also an interesting problem in its own right. I will first cover the rectangular case and then use this result to derive the square case, making heavy use of epsilon nets and anticoncentration inequalities that generalize beyond the sign matrix case. The talk will closely follow Chapter 2.7 of Tao's Topics in Random Matrix theory with some deviation.