Recording date: 30/08/2011
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Beta Ensembles via Gauss Quadrature

In the theory of random matrices, one considers probability distributions on the eigenvalues x1;x2; :::;xn of
an nn Hermitian matrix. For b-ensembles, the probability distribution has the form
P(n) (x1;x2; :::;xn) =
1
C
jV (x1;x2; :::;xn)jb dm (x1)dm (x2) :::dm (xn) ;
where V is the Vandermonde determinant,
V (x1;x2; :::;xn) = Õ
1j<kn
(xk

Doron Lubinsky
Doron Lubinsky