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

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.

References in corpus (6)

• Universal singularity at the closure of a gap in a random matrix theory
• Level Spacing of Random Matrices in an External Source
• Large $n$ limit of Gaussian random matrices with external source, part II
• Large n limit of Gaussian random matrices with external source, part I
• Universality of correlation functions of hermitian random matrices in an external field
• Random hermitian matrices in an external field

Cited by in corpus (3)

• Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
• Spectra of Random Hermitian Matrices with a Small-Rank External Source: The critical and near-critical regimes
• On 2D discrete Schrödinger operators associated with multiple orthogonal polynomials