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SUMMARY:Bulk scaling limit of the Laguerre ensemble - Stephanie Jacquot (C
 ambridge)
DTSTART:20101109T163000Z
DTEND:20101109T173000Z
UID:TALK26755@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:Random matrix theory has found many applications in physics\, 
 statistics and engineering since its inception. The eigenvalues of random 
 matrices are often of particular interest. The standard technique for stud
 ying local eigenvalue behavior of a random matrix distribution involves th
 e following steps. We first choose a family of n x n random matrices which
  we translate and rescale in order to focus on a particular region of the 
 spectrum\, and then we let n \\to\\infty. When this procedure is performed
  carefully\, the limiting eigenvalue behavior often falls into one of thre
 e classes: soft edge\, hard edge or bulk. In the world of random matrices\
 , three ensembles are of particular interest: the Hermite\, Laguerre and J
 acobi \\beta-ensembles. In this talk I will present a joint work with Bene
 dek Valkó. We consider the \\beta-Laguerre ensemble\, a family of distrib
 utions 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 general family of parameters and it is the same a
 s the bulk scaling limit of the corresponding \\beta-Hermite ensemble. \n\
 n\n\nhttp://www.statslab.cam.ac.uk/Dept/People/jacquot.html
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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