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SUMMARY:On fluctuations of eigenvalues of random band matrices - Shcherbin
 a\, M (Institute for Low Temperatures\, Kharkov)
DTSTART:20150622T140000Z
DTEND:20150622T150000Z
UID:TALK59899@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:We consider the fluctuation of linear eigenvalue statistics of
  random band $n$ dimensional matrices\nwhose bandwidth $b$  is assumed to 
 grow with n in such  a way that $b/n$ tends to zero. Without any additiona
 l\nassumptions on the growth of b we prove  CLT for linear eigenvalue stat
 istics for a rather wide class of test\nfunctions.  Thus we remove the  ma
 in technical restriction  $n>>b>>n^{1/2}$ of all the papers\, in which ban
 d matrices\nwere studied before.   Moreover\, the developed method allows 
  to prove automatically the CLT  for linear\n eigenvalue statistics of the
  smooth test functions  for almost all classical models of random matrix t
 heory:\ndeformed Wigner and sample covariance matrices\, sparse matrices\,
  diluted random matrices\, matrices with heavy tales\netc.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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