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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A transportation approach to random matrices. - Fi
galli\, A (University of Texas at Austin)
DTSTART;TZID=Europe/London:20140522T110000
DTEND;TZID=Europe/London:20140522T120000
UID:TALK52744AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52744
DESCRIPTION:Optimal transport theory is an efficient tool to c
onstruct change of variables between probability d
ensities. However\, when it comes to the regularit
y of these maps\, one cannot hope to obtain regula
rity estimates that are uniform with respect to th
e dimension except in some very special cases (for
instance\, between uniformly log-concave densitie
s).\nIn random matrix theory the densities involve
d (modeling the distribution of the eigenvalues) a
re pretty singular\, so it seems hopeless to apply
optimal transport theory in this context. However
\, ideas coming from optimal transport can still b
e used to construct approximate transport maps (i.
e.\, maps which send a density onto another up to
a small error) which enjoy regularity estimates th
at are uniform in the dimension. Such maps can the
n be used to show universality results for the dis
tribution of eigenvalues in 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
CONTACT:Mustapha Amrani
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