Discrete Painlevé equations and random matrix averages

Details Discrete Painlevé equations and random matrix averages Discrete Painlevé equations and random matrix averages

2003-04-13

arxiv.org/abs/math-ph/0304020v1

Physics

Mathematical Physics

25 pages

Scientific paper

10.1088/0951-7715/16/6/303

The $\tau$-function theory of Painlev\'e systems is used to derive recurrences in the rank $n$ of certain random matrix averages over U(n). These recurrences involve auxilary quantities which satisfy discrete Painlev\'e equations. The random matrix averages include cases which can be interpreted as eigenvalue distributions at the hard edge and in the bulk of matrix ensembles with unitary symmetry. The recurrences are illustrated by computing the value of a sequence of these distributions as $n$ varies, and demonstrating convergence to the value of the appropriate limiting distribution.

Affiliated with

Also associated with

No associations

Rating

Discrete Painlevé equations and random matrix averages 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 Discrete Painlevé equations and random matrix averages, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete Painlevé equations and random matrix averages will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-190087