A diffusion description of the random matrix hard edge

Add to your list(s) Download to your calendar using vCal

• Brian Rider (Colorado)
• Tuesday 02 June 2009, 14:00-15:00
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact Berestycki.

With J. Ramirez and B. Virag we recently proved that the limiting soft edge eigenvalues of the general beta ensembles have laws shared by the spectral points of a certain random Schroedinger operator. After recalling this fact I’ll prove there is a similar picture at the random matrix hard edge. That is, the small eigenvalues of sample covariance ensembles are described in terms of a (random) differential operator in the large dimensional limit. Via a Riccati transformation, there is a second description though the hitting distributions of a simple diffusion. The latter picture allows a proof of the anticipated transition between the hard and soft edge laws.

This talk is part of the Probability series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
• Probability
• School of Physical Sciences
• Statistical Laboratory info aggregator
• bld31

Note that ex-directory lists are not shown.