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SUMMARY:Giorgio Cipolloni (IST Austria)
DTSTART:20210205T130000Z
DTEND:20210205T140000Z
DTSTAMP:20260423T022713Z
UID:MEGA/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MEGA/18/">Co
 rrelated DBMs and fluctuations in the circular law: CLT for i.i.d. random 
 matrices.</a>\nby Giorgio Cipolloni (IST Austria) as part of Séminaire ME
 GA\n\n\nAbstract\nWe consider a large non-Hermitian i.i.d. matrix X with r
 eal or complex entries and show that the linear statistics of the eigenval
 ues are asymptotically Gaussian for test function having 2+\\epsilon deriv
 atives. Previously this result was known only for the Ginibre ensemble\, w
 here explicit formulas for the correlation functions are available\, and e
 nsembles close to Ginibre in the sense of moment matching\; our result hol
 ds for general distribution of the matrix entries. The proof relies on two
  main novel ingredients: (i) local law for product of resolvents of the He
 rmitisation of X at two different spectral parameters\, (ii) coupling of s
 everal dependent Dyson Brownian motions.\n
LOCATION:https://researchseminars.org/talk/MEGA/18/
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