Painleve IV and degenerate Gaussian Unitary Ensembles

Details Painleve IV and degenerate Gaussian Unitary Ensembles Painleve IV and degenerate Gaussian Unitary Ensembles

2006-06-28

arxiv.org/abs/math-ph/0606064v1

Physics

Mathematical Physics

17 pages

Scientific paper

10.1088/0305-4470/39/40/007

We consider those Gaussian Unitary Ensembles where the eigenvalues have prescribed multiplicities, and obtain joint probability density for the 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 Painleve 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.

Affiliated with

Also associated with

No associations

Rating

Painleve IV and degenerate Gaussian Unitary Ensembles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Painleve IV and degenerate Gaussian Unitary Ensembles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Painleve IV and degenerate Gaussian Unitary Ensembles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-535497