Event Date
Speaker: Arup Bose (Professor of Theoretical Statistics and Mathematics, Indian Statistical Institute, Kolkata)
Title: "Limiting spectral distribution of random matrices with independent entries"
Abstract:
It is well known that the limit eigenvalue distribution of the scaled standard Wigner matrix is the semi-circular distribution whose 2kth moment equals the number of noncrossing pair-partitions of {1. 2...., 2k}. There are several extensions of this result in the literature, including the sparse case. We discuss extension of these results by relaxing significantly the i.i.d. assumption. The limiting spectral distribution then involve a larger class of partitions. In the process we show how some new sets of partitions gain importance. Several existing and new results for their band and sparse versions, as well as for matrices with continuous and discrete variance profile follow as special cases.
Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have also been studied quite extensively. Under the assumption that the entries are taken from an i.i.d. sequence with finite variance, the LSD are tied together by a common thread —the 2kth moment of the limit equals a weighted sum over different types of pair-partitions of the set f1, 2, ..., 2k} and are universal. Some results are also known for the sparse case. Time permitting we show suitable extension of these results also, along the lines of the Wigner matrix.
Seminar date/time: Tuesday June 6, 2023 at 4:10pm
Location: MSB 1147 (Colloquium Room). Refreshments 3:30pm.