Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-04-10
Nucl.Phys.B664:457-476,2003
Physics
High Energy Physics
High Energy Physics - Theory
18 pages
Scientific paper
10.1016/S0550-3213(03)00458-9
It has been shown recently [10] that Cauchy transforms of orthogonal polynomials appear naturally in general correlation functions containing ratios of characteristic polynomials of random NxN Hermitian matrices. Our main goal is to investigate the issue of universality of large N asymptotics for those Cauchy transforms for a wide class of weight functions. Our analysis covers three different scaling regimes: the "hard edge", the "bulk" and the "soft edge" of the spectrum, thus extending the earlier results known for the bulk. The principal tool is to show that for finite matrix size N the auxiliary "wave functions" associated with the Cauchy transforms obey the same second order differential equation as those associated with the orthogonal polynomials themselves.
Akemann Gernot
Fyodorov Yan V.
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