Hadamard product of random matrices and their limiting spectral distributions

Abstract: In this talk I shall present the limiting spectral distributions of the Hadamard products of random matrices GUEs. In certain scenarios, the limiting spectral distributions of such random matrix models exist and can be described in terms of square free convolutions. One related question to square free additive convolution is to investigate when the multiplicative convolution of the semi-circular law and a probability law on the positive real line has a semi-circular law as a component in the free additive convolution. We shall answer this question by offering necessary and sufficient conditions. This is joint work with Ming Hsiao.

Mathematics

Audience: learners

Trends in Mathematical Research