Asymptotics of orthogonal polynomials and eigenvalue distribution of random matrices

Анотація

We present an informal discussion of recent results on the asymptotic behaviour of orthogonal polynomials, in particular orthogonal polynomials with varying weight, emphasizing links with spectral theory. We apply some of these results to find the leading term of the covariance of linear statistics of certain unitary invariant ensembles of random matrix of large order.