Fluctations of the empirical law of large random matrices. (Fluctations de la loi empirique de grandes matrices aléatoires.) (French) Zbl 1016.15020

Cabanal-Duvillard, Thierry

Ann. Inst. Henri Poincaré, Probab. Stat. 37, No. 3, 373-402 (2001).

The author investigates fluctuations of the empirical law of large random matrices around the limits when the size goes to infinity, with the help of stochastic calculus. By using these results he deals with the non-commutative case of two independent Wigner matrices.
In Section 1, he states primary results on the Wigner matrix using the Ito formula and Chebyshev polynomials. In Section 3 he dicusses the fluctuations for two matrices, generalizing the Ito formula for a double Hermitian process and using stochastic calculus.

Reviewer: T.Nôno (Hiroshima)

MSC:

15B52	Random matrices (algebraic aspects)
60F05	Central limit and other weak theorems

Keywords:

central limit theorem; empirical law; large random matrices; Wigner matrices; Ito formula; fluctuations; Hermitian process