Physics – Mathematical Physics
Scientific paper
2000-03-29
Physics
Mathematical Physics
41 pages, submitted to Commun. Math. Phys
Scientific paper
10.1007/s002200000264
Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices $A_{n}$ and $B_{n}$ rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix $U_{n}$ (i.e. $A_{n}+U_{n}^{\ast}B_{n}U_{n}$) is studied in the limit of large matrix order $n$. Convergence in probability to a limiting nonrandom measure is established. A functional equation for the Stieltjes transform of the limiting measure in terms of limiting eigenvalue measures of $A_{n}$ and $B_{n}$ is obtained and studied. Keywords: random matrices, eigenvalue distribution
Pastur Leonid
Vasilchuk Vladimir
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