Random hermitian matrices in an external field
Abstract
In this article, a model of random hermitian matrices is considered, in which the measure (-S) contains a general U(N)-invariant potential and an external source term: S=N(V(M)+MA). The generalization of known determinant formulae leads to compact expressions for the correlation functions of the energy levels. These expressions, exact at finite N, are potentially useful for asymptotic analysis.
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