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SUMMARY:From the mesoscopic to microscopic scale in random matrix theory -
  Bourgade\, P (Courant Institute of Mathematical Sciences)
DTSTART:20150622T123000Z
DTEND:20150622T133000Z
UID:TALK59901@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Co-authors: Laszlo Erdos (IST)\, Horng Tzer Yau (Harvard)\, Ju
 n Yin (Wisconsin Madison) \n\nEugene Wigner has envisioned that the distri
 butions of the eigenvalues of large Gaussian random matrices are new parad
 igms for universal statistics of large correlated quantum systems. These r
 andom matrix eigenvalues statistics supposedly occur together with delocal
 ized eigenstates. I will explain recent developments proving this paradigm
  for eigenvalues and eigenvectors of random matrices. This is achieved by 
 bootstrap on scales\, from mesoscopic to microscopic. Random walks in rand
 om environments\, homogenization and the coupling method play a key role.\
 n
LOCATION:Seminar Room 1\, Newton Institute
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