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SUMMARY:A transportation approach to random matrices. - Figalli\, A (Unive
 rsity of Texas at Austin)
DTSTART:20140522T100000Z
DTEND:20140522T110000Z
UID:TALK52744@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Optimal transport theory is an efficient tool to construct cha
 nge of variables between probability densities. However\, when it comes to
  the regularity of these maps\, one cannot hope to obtain regularity estim
 ates that are uniform with respect to the dimension except in some very sp
 ecial cases (for instance\, between uniformly log-concave densities).\nIn 
 random matrix theory the densities involved (modeling the distribution of 
 the eigenvalues) are pretty singular\, so it seems hopeless to apply optim
 al transport theory in this context. However\, ideas coming from optimal t
 ransport can still be used to construct approximate transport maps (i.e.\,
  maps which send a density onto another up to a small error) which enjoy r
 egularity estimates that are uniform in the dimension. Such maps can then 
 be used to show universality results for the distribution of eigenvalues i
 n random matrices.\nThe aim of this talk is to give a self-contained prese
 ntation of these results.\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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