On a limiting distribution of singular values of random band matrices

A. Lytova^a, L. Pastur<sup>b

a</sup> Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
^b B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine

Abstract: 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.

Key words and phrases: random band matrices, triangular matrices, limiting distribution of singular values.

MSC: Primary 60B10, 60B20; Secondary 15B52, 15A18

Received: 23.04.2015

Language: English

DOI: 10.15407/mag11.04.311

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