Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles

Details Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles

2000-05-30

arxiv.org/abs/nlin/0005064v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages

Scientific paper

The scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles is evaluated in terms of a Painlev\'e V transcendent. This same Painlev\'e V transcendent is known from the work of Tracy and Widom, where it has been shown to specify the scaled distribution of the smallest eigenvalue in the Laguerre unitary ensemble. The starting point for our calculation is the scaled $k$-point distribution of every odd labelled eigenvalue in two superimposed Laguerre orthogonal ensembles.

Affiliated with

Also associated with

No associations

Rating

Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic 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 Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-636733