Singular values of random band matrices: Marchenko-Pastur law and more
We consider the limiting spectral distribution of matrices of the form (R+X)(R+X)^∗/(2b_n+1), where X is an n by n band matrix of bandwidth b_n and R is a non random band matrix of bandwidth b_n. We show that the Stieltjes transform of spectrum of such matrices converges to the Stieltjes transform of a non-random measure. And the limiting Stieltjes transform satisfies an integral equation. For R=0, the integral equation yields the Stieltjes transform of the Marchenko-Pastur law. This is a joint work with Indrajit Jana.