Probability Seminar
Speaker: Sunita Rani, School of Basic Sciences (Mathematics), IIT Bhubaneswar
Host: Koushik Saha
Title: Spectrum of Inter-Correlated Random Matrices
Time, day and date: 5:00:00 PM - 6:00:00 PM, Tuesday, July 28
Venue: Online (meet.google.com/gdd-yimr-gds)
Abstract: In this talk, we study the central limit theorem (CLT) for linear eigenvalue statistics (LES) of several classes of random matrices for different types of test functions. We establish CLTs for various structured random matrix ensembles, including complex- and real-valued centrosymmetric matrices. For centrosymmetric matrices, we also develop combinatorial techniques to compute the asymptotic moments and the variance of the limiting Gaussian distribution. Furthermore, we establish the CLT for LES of correlated non-Hermitian block matrices, where the limiting fluctuations depend on the correlation structure of the matrix entries. All these results are obtained under suitable bounded moment assumptions.
We then extend the analysis to random matrices with exploding moments, where the moments of the matrix entries grow with the matrix dimension. In this setting, we study the asymptotic behavior and the CLT for normalized traces of several matrix models, including elliptic matrices, non-Hermitian matrices, correlated non-Hermitian block matrices, centrosymmetric matrices, and circulant matrices.