The Third Jyotiprasad Medhi Memorial Annual Lecture was delivered by Prof. Arup Bose, Indian Statistical Institute, Kolkata on September 27 at 4:15 PM.

Title of the Lecture: Asymptotics of Large Dimensional Random Matrices and its uses in Statistical Analysis

Venue: Lecture Hall 4, IIT Guwahati

Abstract:

Though the area of random matrices has grown rapidly within physics and mathematics, it is interesting to note that its rst appearance was in Statis- tics. In the last couple of decades theory and applications of random matrices has grown enormously across many diㄦent scientic disciplines, for exam- ple in nuclear physics, operator theory, wireless communications, probability, and non-commutative probability. Though large dimensional random matri- ces (LDRM) has been gaining some attention in high dimensional statistics, statisticians by and large have remained unfamiliar with various aspects of LDRM.

The goal of this lecture is to quickly introduce a variety of asymptotic results for sequences of LDRM, specially from the point of view of the be- haviour of the limit spectrum of one or more sequences of random matrices, and point out some potential applications in statistics.

In particular, we hope to discuss some symmetric high dimensional random matrices (such as the Wigner matrix, the sample covariance and symmetrised polynomials of covariance matrices and auto-covariance matrices), and some non-symmetric high dimensional matrices (such as the Circulant matrix, the i.i.d. matrix and the auto-covariance matrix).

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