Eigenvalue density in Hermitian matrix models by the Lax pair method

In this paper, a new method is discussed to derive the eigenvalue density in a Hermitian matrix model with a general potential. The density is considered on one interval or multiple disjoint intervals. The method is based on Lax pair theory and the Cayley-Hamilton theorem by studying the orthogonal...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 42; no. 20; pp. 205205 - 205205 (25)
Main Authors McLeod, J B, Wang, C B
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 22.05.2009
IOP
Subjects
Exact sciences and technology
Physics
Riemann problem
Hilbert problem
Painlevé equation
Density matrix
Hermitian matrix
Eigenvalues
Models
Orthogonal polynomial
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Summary:In this paper, a new method is discussed to derive the eigenvalue density in a Hermitian matrix model with a general potential. The density is considered on one interval or multiple disjoint intervals. The method is based on Lax pair theory and the Cayley-Hamilton theorem by studying the orthogonal polynomials associated with the Hermitian matrix model. It is obtained that the restriction conditions for the parameters in the density are connected to the discrete Painleve I equation, and the results are related to the scalar Riemann-Hilbert problem. Some special density functions are also discussed in association with the known results in this subject.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/42/20/205205