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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20260215T152113Z
DTSTART:20260225T160000Z
DTEND:20260225T170000Z
SUMMARY:Probability Seminar: Indrajit Jana - CLT for LES of correlated No
 n-Hermitian Random Matrices
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}c1nt-mlnw7s
 zp-h0n5gg
DESCRIPTION:Indrajit Jana (IIT Bhubaneswar) will speak at the Probability
  seminar.\n\n\nTitle: CLT for LES of correlated Non-Hermitian Random Mat
 rices\n\nAbstract: In this talk\, We consider two (or finitely many) $n\
 \times n$ non-Hermitian random matrices such that the $ij$th entry of on
 e matrix is correlated with the $ij$th entry of the other matrix. Howeve
 r\, the entries of any particular matrix are i.i.d. random variables. We
  study the asymptotic behavior of the combined spectrum\, and the limit 
 of the linear eigenvalue statistic defined on the combined spectrum. We 
 show that if the random variables are centered with variance $1/n$ and h
 ave finite moments\, then the centered Linear Eigenvalue Statistics (LES
 s) converge jointly to a bivariate Gaussian distribution. We assumed tha
 t the test function used in the LES belongs to Sobolev $H^{2+\\varrho}$ 
 space. The variance of the limiting Gaussian distribution depends on cor
 relation structure of the matrix entries and the fourth order mixed cumu
 lants of the matrix entries. If time permits\, we shall discuss the effe
 ct of heavy tailed distributions on such results.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 2\, Alan Turing Building\, Manchester
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