Probability Seminar: Indrajit Jana - CLT for LES of correlated Non-Hermitian Random Matrices
| Dates: | 25 February 2026 |
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| Times: | 16:00 - 17:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Indrajit Jana (IIT Bhubaneswar) will speak at the Probability seminar.
Title: CLT for LES of correlated Non-Hermitian Random Matrices
Abstract: In this talk, We consider two (or finitely many) $n\times n$ non-Hermitian random matrices such that the $ij$th entry of one matrix is correlated with the $ij$th entry of the other matrix. However, 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 have finite moments, then the centered Linear Eigenvalue Statistics (LESs) converge jointly to a bivariate Gaussian distribution. We assumed that the test function used in the LES belongs to Sobolev $H^{2+\varrho}$ space. The variance of the limiting Gaussian distribution depends on correlation structure of the matrix entries and the fourth order mixed cumulants of the matrix entries. If time permits, we shall discuss the effect of heavy tailed distributions on such results.
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Frank Adams 2
Alan Turing Building
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