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SUMMARY:The eigenvectors of non-Hermitian matrices
DTSTART:20231208T130000Z
DTEND:20231208T141500Z
DTSTAMP:20260610T234500Z
UID:indico-event-10164@indico.math.cnrs.fr
CONTACT:guillaume.barraquand@math.cnrs.fr
DESCRIPTION:Speakers: Simon Coste\n\nAbstract : This talk will be a genera
 l presentation on eigenvectors of non-Hermitian models of random matrices\
 , especially the Gaussian ensembles. We will start by reviewing what is kn
 own on the complex Ginibre ensemble\, and especially the results by Chalke
 r and Mehlig (2000) and Bourgade and Dubach (2018) on the overlaps between
  left and right eigenvectors. The case of the real Ginibre ensemble is sur
 prisingly different. I will describe the law of the real Schur decompositi
 on of real Ginibre matrices (due to Edelman\, 1997) and how it can be used
  to study certain statistics of the eigenvectors\, notably (i) the overlap
 s between eigenvectors associated to real eigenvalues (recent results due 
 to Würfel\, Crumpton and Fyodorov\, 23+) and (ii) the inverse kurtosis of
  every bulk eigenvector\, which is a measure their level of delocalization
 . In particular I will show that\, even though all the eigenvectors are de
 localized\, those associated to eigenvalues close to the real axis are sli
 ghtly more localized\, and I will give the exact limiting distribution of 
 the inverse kurtosis in the thermodynamic limit. This is based on ongoing 
 work with Lucas Benigni and Guillaume Dubach.\n\nhttps://indico.math.cnrs.
 fr/event/10164/
LOCATION:Salle Mirzakhani (201)
URL:https://indico.math.cnrs.fr/event/10164/
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