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UID:1-246@lptms.universite-paris-saclay.fr
DTSTART:20140321T110000Z
DTEND:20140321T121500Z
DTSTAMP:20140314T080543Z
URL:https://www.lptms.universite-paris-saclay.fr/seminars/seminaire-except
 ionnel-maciej-nowak/
SUMMARY:Séminaire exceptionnel : Maciej Nowak - LPTMS\, salle 201\, 2ème 
 étage\, Bât 100\, Campus d'Orsay - 21 Mar 14 11:00
DESCRIPTION:"Burgers dynamics  in hermitian and nonhermitian RMM".\nMaciej
  Nowak\, Jagellonian University\, Cracovie.\n \nWe obtain several classes
  of non-linear partial differential equations for various random matrix en
 sembles undergoing Brownian type of random walk. These equations for spect
 ral flow of eigenvalues as a function of dynamical parameter ("time") are 
 exact for any finite size N of the random matrix ensemble and resemble vis
 cid Burgers-like equations known in the theory of turbulence. In the limit
  of infinite size of the matrix\, these equations reduce complex inviscid 
 Burgers equations\, proposed originally by Voiculescu in the context of fr
 ee processes. We identify spectral shock waves for these equations in the 
 limit of the infinite size of the matrix\, and then we solve exact\, finit
 e N nonlinear equations in the vicinity of the shocks\, obtaining in this 
 way universal\, microscopic scalings equivalent to Airy\, Bessel and cuspo
 id kernels. Finally\, we show that similar but  hidden Burgers-like struc
 tures appear (surprisingly)  also in nonhermitian random matrix models\, 
 e.g. in the Ginibre-Girko ensemble\, where they govern the concurent  evo
 lution of both eigenvalues and eigenvectors. 
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15 
 Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
 me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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