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Asymptotic analysis of random matrices with external source and a family of algebraic curves

K. D. T-R McLaughlin
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Abstract

We present a set of conditions which, if satisfied, provide for a complete asymptotic analysis of random matrices with source term containing two distinct eigenvalues. These conditions are shown to be equivalent to the existence of a particular algebraic curve. For the case of a quartic external field, the curve in question is proven to exist, yielding precise asymptotic information about the limiting mean density of eigenvalues, as well as bulk and edge universality.

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K. D. T-R McLaughlin. 2006-10-20. Asymptotic analysis of random matrices with external source and a family of algebraic curves. https://doi.org/10.1088/0951-7715%2F20%2F7%2F002

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