Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-04-03
J.Statist.Phys. 94 (1999) 347-364
Physics
High Energy Physics
High Energy Physics - Theory
13 pages. LaTeX file. Improved and simplified derivations of results
Scientific paper
For the unitary ensembles of $N\times N$ Hermitian matrices associated with a weight function $w$ there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For the orthogonal and symplectic ensembles of Hermitian matrices there are $2\times2$ matrix kernels, usually constructed using skew-orthogonal polynomials, which play an analogous role. These matrix kernels are determined by their upper left-hand entries. We derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles. We also show that whenever $w'/w$ is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of $w'/w$. General formulas are obtained for these extra terms. We do not use skew-orthogonal polynomials in the derivations.
No associations
LandOfFree
On the relation between orthogonal, symplectic and unitary matrix 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 On the relation between orthogonal, symplectic and unitary matrix ensembles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the relation between orthogonal, symplectic and unitary matrix ensembles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-348477