Painlevé IV and degenerate Gaussian unitary ensembles

Chen, Y. and Feigin, M. (2006) Painlevé IV and degenerate Gaussian unitary ensembles. Journal of Physics A: Mathematical and General, 39(40), pp. 12381-12393. (doi:10.1088/0305-4470/39/40/007)

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Publisher's URL: http://dx.doi.org/10.1088/0305-4470/39/40/007

Abstract

We consider those Gaussian unitary ensembles where the eigenvalues have prescribed multiplicities, and obtain joint probability density for eigenvalues. In the simplest case where there is only one multiple eigenvalue t, this leads to orthogonal polynomials with the Hermite weight perturbed by a factor that has a multiple zero at t. We show through a pair of ladder operators, that the diagonal recurrence coefficients satisfy a particular Painlevé IV equation for any real multiplicity. If the multiplicity is even they are expressed in terms of the generalized Hermite polynomials, with t as the independent variable.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Feigin, Dr Misha
Authors: Chen, Y., and Feigin, M.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Physics A: Mathematical and General
Publisher:Institute of Physics Publishing Ltd.
ISSN:0305-4470

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