Geodesic
Asymptotic distribution of singular values for matrices in a spherical ensemble
Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 169-200

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the asymptotic behavior of the singular values of a so-called spherical ensemble of random matrices of large dimension. These are matrices of the form $\mathbf X\mathbf Y^{-1}$, where $\mathbf X$ and $\mathbf Y$ are independent matrices of dimension $n\times n$ whose symmetric entries have correlation coefficient $\rho$. We show that the limit distribution of the singular values is independent of the correlation coefficient and has the density $$ p(x)=\frac1{\pi\sqrt x(1+x)}\mathbb I\{x>0\}, $$ where $\mathbb I\{A\}$ stands for the indicator of an event $A$. 
@article{MT_2013_16_2_a9,
     author = {A. N. Tikhomirov},
     title = {Asymptotic distribution of singular values for matrices in a spherical ensemble},
     journal = {Matemati\v{c}eskie trudy},
     pages = {169--200},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2013_16_2_a9/}
}
TY  - JOUR
AU  - A. N. Tikhomirov
TI  - Asymptotic distribution of singular values for matrices in a spherical ensemble
JO  - Matematičeskie trudy
PY  - 2013
SP  - 169
EP  - 200
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2013_16_2_a9/
LA  - ru
ID  - MT_2013_16_2_a9
ER  - 
%0 Journal Article
%A A. N. Tikhomirov
%T Asymptotic distribution of singular values for matrices in a spherical ensemble
%J Matematičeskie trudy
%D 2013
%P 169-200
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2013_16_2_a9/
%G ru
%F MT_2013_16_2_a9
A. N. Tikhomirov. Asymptotic distribution of singular values for matrices in a spherical ensemble. Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 169-200. http://geodesic.mathdoc.fr/item/MT_2013_16_2_a9/