Geodesic
On a limiting distribution of singular values of random band matrices
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015), pp. 311-332.

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An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to infinity. Conditions under which this limit agrees with the quarter-circle law are found. An interesting particular case of lower triangular random matrices is also considered and certain properties of the corresponding limiting singular value distribution are given. 
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A. Lytova; L. Pastur. On a limiting distribution of singular values of random band matrices. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015), pp. 311-332. http://geodesic.mathdoc.fr/item/JMAG_2015_11_a0/

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