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. 
@article{JMAG_2015_11_a0,
     author = {A. Lytova and L. Pastur},
     title = {On a limiting distribution of singular values of random band matrices},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {311--332},
     publisher = {mathdoc},
     volume = {11},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2015_11_a0/}
}
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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/