Distribution of singular values of random band matrices; Marchenko-Pastur law and more
| Autor: | Jana, Indrajit, Soshnikov, Alexander |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10955-017-1844-5 |
| Popis: | 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 ESD 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. Comment: Many typos are corrected. Statement and the proofs of the main theorems are written in a more elaborated way |
| Databáze: | arXiv |
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