ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 46, 60 Vasylchuk Volodymyr, Institute for Low Temperature Physics, Ukraine Pastur Leonid, Université Paris7, France; Institute for Low Temperature Physics, Ukraine On the Law of Addition of Random Matrices. Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices A and B rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix U (i. e. A + U^{†}BU) is studied in the limit of large matrix order. 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 measures of A and B is obtained and studied. In the case of bounded supports of limiting measures of A and B this result was obtained by R. Speicher. Reference: R. Speicher, Free Convolution and the Random Sum of Matrices, Publ. Res. Inst. Math. Sci. 29 (1993), 731–744