On the Law of Addition of Random Matrices

@inproceedings{Pastur2000OnTL,
  title={On the Law of Addition of Random Matrices},
  author={Luc Pastur and V. Vasilchuk},
  year={2000}
}
Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices An and Bn rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix Un (i.e. An + U ∗ n BnUn) 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 An and Bn is… CONTINUE READING

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