Abstract
We present a set of conditions which, if satisfied, provide for a complete asymptotic analysis of random matrices with a 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.
| Original language | English (US) |
|---|---|
| Article number | 002 |
| Pages (from-to) | 1547-1571 |
| Number of pages | 25 |
| Journal | Nonlinearity |
| Volume | 20 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 1 2007 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
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