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SUMMARY:A diffusion description of the random matrix hard edge - Brian Rid
 er (Colorado)
DTSTART:20090602T130000Z
DTEND:20090602T140000Z
UID:TALK17739@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:With J. Ramirez and B. Virag we recently proved that the limit
 ing soft edge eigenvalues of the general beta ensembles have laws shared b
 y the spectral points of a certain random Schroedinger operator. After rec
 alling this fact I'll prove there is a similar picture at the random matri
 x hard edge. That is\, the small eigenvalues of sample covariance ensemble
 s are described in terms of a (random) differential operator in the large 
 dimensional limit. Via a Riccati transformation\, there is a second descri
 ption though the hitting distributions of a simple diffusion. The latter p
 icture allows a proof of the anticipated transition between the hard and s
 oft edge laws. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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