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Regular version of the site

Article

ON A GENERALIZATION OF THE ELLIPTIC LAW FOR RANDOM MATRICES

Acta Physica Polonica, Series B.. 2015. Vol. 46. No. 9. P. 1737-1745.
Naumov A., Tikhomirov A., Гётце Ф.

We consider the products of m ≥ 2 independent large real random ma- trices with independent tuples (X_{jk}^(q),X_{kj}^(q)), 1 ≤ j < k ≤ n of entries. The X_{jk}^(q), X_{kj}^{(q) entries are standardized and correlated with correlation coefficient ρ. The limit distribution of the empirical spectral distribution of the eigenvalues of such products does not depend on ρ and is equal to the distribution of the mth power of a uniformly distributed random variable on the unit disc.