Diffusion at the random matrix hard edge

Details Diffusion at the random matrix hard edge Diffusion at the random matrix hard edge

2008-03-13

arxiv.org/abs/0803.2043v4

Mathematics

Probability

(More) typos corrected, added references

Scientific paper

10.1007/s00220-008-0712-1

We show that the limiting minimal eigenvalue distributions for a natural generalization of Gaussian sample-covariance structures (the "beta ensembles") are described by the spectrum of a random diffusion generator. By a Riccati transformation, we obtain a second diffusion description of the limiting eigenvalues in terms of hitting laws. This picture pertains to the so-called hard edge of random matrix theory and sits in complement to the recent work of the authors and B. Virag on the general beta random matrix soft edge. In fact, the diffusion descriptions found on both sides are used here to prove there exists a transition between the soft and hard edge laws at all values of beta.

Affiliated with

Also associated with

No associations

Rating

Diffusion at the random matrix hard edge 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 Diffusion at the random matrix hard edge, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diffusion at the random matrix hard edge will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-246133