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UID:20260415T075916EDT-1023mJUvew@132.216.98.100
DTSTAMP:20260415T115916Z
DESCRIPTION:Title: The Eigenvalues of Brownian Motions on GL(N\,C)\n\nAbstr
 act: The study of the empirical law of eigenvalues of a random matrix is a
 n important step in understanding its asymptotic behaviour. But while in t
 he self-adjoint or normal case the proof is often straightforward\, stream
 lined by a collection of existing results\, in the general case it is usua
 lly an especially tricky problem due to the necessary use of the so-called
  Brown measure. The aim of this talk is to investigate one of those models
 . In the late nineties\, Philippe Biane studied the asymptotic behaviour o
 f Brownian motions on Lie Group. While in the unitary case he fully descri
 bed their limit and proved the convergence\, in the case of GL(N\,C)\, thi
 s problem remained open until recently\, where we managed to prove it in i
 ts entirety. This talk will be divided into three part\, first an introduc
 tion to explain the difficulties arising from handling the Brown measure\,
  then an explanation of the model and the result that we prove\, and final
 ly some elements of proof. In particular\, one of the key element to this 
 proof is a new approach to computing matrix integrals with the help of fre
 e probability that has yielded pretty general results in the last few year
 s. This talk is based on a joint work ( https://arxiv.org/pdf/2511.10535 )
  with Tatiana Brailovskaya\, Nicholas Cook\, and Todd Kemp.\n
DTSTART:20260212T213000Z
DTEND:20260212T223000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Felix Parraud (Queen's)
URL:https://www.mcgill.ca/mathstat/channels/event/felix-parraud-queens-3711
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