Asymptotics of orthogonal polynomials and eigenvalue distribution of random matrices

L. Pastur

Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov, 61103, Ukraine

Abstract: 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.

MSC: 42C05, 47B35, 60B15

Received: 04.03.2002

Language: English

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