Determinants of random matrices and jack polynomials of rectangular shape

G. E. Andrews, I. P. Goulden, D. M. Jackson

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We consider an N-dimensional real integral, indexed by a parameter that specifies the power of a Vandermonde determinant. For two particular values of the parameter, this integral arises from matrix integrals, over real symmetric and complex Hermitian N × N matrices. When it is normalized, it gives the expectation of an arbitrary power of the determinant. The results are given as finite summations, using terminating hypergeometric series. We relate the integral to a specific coefficient in the Jack polynomial indexed by a partition of rectangular shape, and present data for this coefficient in terms of the parameter α.

Original languageEnglish (US)
Pages (from-to)377-390
Number of pages14
JournalStudies in Applied Mathematics
Volume110
Issue number4
DOIs
StatePublished - May 1 2003

Fingerprint

Jack Polynomials
Random Polynomials
Jacks
Matrix Polynomial
Random Matrices
Determinant
Polynomials
Vandermonde determinant
Hypergeometric Series
Coefficient
Summation
Partition
Arbitrary

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

Andrews, G. E. ; Goulden, I. P. ; Jackson, D. M. / Determinants of random matrices and jack polynomials of rectangular shape. In: Studies in Applied Mathematics. 2003 ; Vol. 110, No. 4. pp. 377-390.
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Determinants of random matrices and jack polynomials of rectangular shape. / Andrews, G. E.; Goulden, I. P.; Jackson, D. M.

In: Studies in Applied Mathematics, Vol. 110, No. 4, 01.05.2003, p. 377-390.

Research output: Contribution to journalArticle

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