2019/08/12 by Che, Ziliang, Lopatto, Patrick
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1908.04060
We consider the least singular value of M = R^* X T + U^* YV, where R,T,U,V are independent Haar-distributed unitary matrices and X, Y are deterministic diagonal matrices. Under weak conditions on X and Y, we show that the limiting distribution of the least singular value of M, suitably rescaled, is the same as the limiting distribution for the least singular value of a matrix of i.i.d. gaussian random variables. Our proof is based on the dynamical method used by Che and Landon to study the local spectral statistics of sums of Hermitian matrices.