Eigenvalues of Wigner Matrices: A dip into Random Matrix Theory

In this talk I’ll present one of the most fundamental results in Random Matrix Theory: the convergence in distribution of the empirical law of the eigenvalues of a Wigner matrix to the semicircle distribution. This is a classical result dating to the founding of the subject. The proof is elementary and use the convergence of the random moments of the empirical law to those given by the semicircle distribution. This convergence is accomplished by a combinatorial argument.