ESD of singular values of random band matrices; Marchenko-Pastur law and more
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ESD of singular values of random band matrices; Marchenko-Pastur law and more

  • Author(s): Jana, Indrajit
  • Soshnikov, Alexander
  • et al.

Published Web Location

https://arxiv.org/pdf/1610.02153.pdf
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Abstract

We consider the limiting spectral distribution of matrices of the form $\frac{1}{2b_{n}+1} (R + X)(R + X)^{*}$, where $X$ is an $n\times n$ 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

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