Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $β=2$

Details Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $β=2$ Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $β=2$

2011-09-23

arxiv.org/abs/1109.5109v2

Physics

Mathematical Physics

14 pages; PACS: 02.10.Yn, 02.50.-r, 05.90.+m, 12.38.-t

Scientific paper

In the past decades, determinants and Pfaffians were found for eigenvalue correlations of various random matrix ensembles. These structures simplify the average over a large number of ratios of characteristic polynomials to integrations over one and two characteristic polynomials only. Up to now it was thought that determinants occur for ensembles with Dyson index $\beta=2$ whereas Pfaffians only for ensembles with $\beta=1,4$. We derive a non-trivial Pfaffian determinant for $\beta=2$ random matrix ensembles which is similar to the one for $\beta=1,4$. Thus, it unveils a hidden universality of this structure. We also give a general relation between the orthogonal polynomials related to the determinantal structure and the skew-orthogonal polynomials corresponding to the Pfaffian. As a particular example we consider the chiral unitary ensembles in great detail.

Affiliated with

Also associated with

No associations

Rating

Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $β=2$ 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 Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $β=2$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $β=2$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-724326