Search results for "random band matrices"

On a limiting distribution of singular values of random band matrices

2015

An equation is obtained for the Stieltjes transform of the normalized dis- tribution 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 matri- ces is also considered and certain properties of the corresponding limiting singular value distribution are given.