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CATEGORIES:Statistical Laboratory Graduate Seminars
SUMMARY:Random matrices - Stephanie Jacquot (Statslab)
DTSTART;TZID=Europe/London:20110224T151500
DTEND;TZID=Europe/London:20110224T160000
UID:TALK29655AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29655
DESCRIPTION:Random matrix theory has found many applications i
n physics\, statistics and engineering since its i
nception. The eigenvalues of random matrices are o
ften of particular interest. The standard techniqu
e for studying local eigenvalue behavior of a rand
om matrix distribution involves the following step
s. We first choose a family of n x n random matric
es which we translate and rescale in order to focu
s on a particular region of the spectrum\, and the
n we let n tend to infinity. When this procedure i
s performed carefully\, the limiting eigenvalue be
havior often falls into one of three classes: soft
edge\, hard edge or bulk. In the world of random
matrices\, three ensembles are of particular inter
est: the Hermite\, Laguerre and Jacobi beta-ensemb
les. In this talk I will present a joint work with
Benedek Valkó. We consider the beta-Laguerre ense
mble\, a family of distributions generalizing the
joint eigenvalue distribution of the Wishart rando
m matrices. We show that the bulk scaling limit of
these ensembles exists for all beta > 0 for a gen
eral family of parameters and it is the same as th
e bulk scaling limit of the corresponding beta-Her
mite ensemble.
LOCATION:CMS\, MR4
CONTACT:Elena Yudovina
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