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

K. T.R. McLaughlin

doi:10.1088/0951-7715/20/7/002

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

K. T.R. McLaughlin

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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	https://doi.org/10.1088/0951-7715/20/7/002
State	Published - Jul 1 2007

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

Access to Document

10.1088/0951-7715/20/7/002

Cite this

@article{2d55a59e6fa642ae815e2c746ccb1cb2,

title = "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 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.",

author = "McLaughlin, {K. T.R.}",

year = "2007",

month = jul,

day = "1",

doi = "10.1088/0951-7715/20/7/002",

language = "English (US)",

volume = "20",

pages = "1547--1571",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "IOP Publishing Ltd.",

number = "7",

}

TY - JOUR

T1 - Asymptotic analysis of random matrices with external source and a family of algebraic curves

AU - McLaughlin, K. T.R.

PY - 2007/7/1

Y1 - 2007/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34250640349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250640349&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/20/7/002

DO - 10.1088/0951-7715/20/7/002

M3 - Article

AN - SCOPUS:34250640349

SN - 0951-7715

VL - 20

SP - 1547

EP - 1571

JO - Nonlinearity

JF - Nonlinearity

IS - 7

M1 - 002

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this