Bulk behaviour of Schur-Hadamard products of symmetric random matrices
Probability
2014-03-18 v2
Abstract
We develop a general method for establishing the existence of the Limiting Spectral Distributions (LSD) of Schur-Hadamard products of independent symmetric patterned random matrices. We apply this method to show that the LSDs of Schur-Hadamard products of some common patterned matrices exist and identify the limits. In particular, the Schur-Hadamard product of independent Toeplitz and Hankel matrices has the semi-circular LSD. We also prove an invariance theorem that may be used to find the LSD in many examples.
Keywords
Cite
@article{arxiv.1402.2207,
title = {Bulk behaviour of Schur-Hadamard products of symmetric random matrices},
author = {Arup Bose and Soumendu Sundar Mukherjee},
journal= {arXiv preprint arXiv:1402.2207},
year = {2014}
}
Comments
27 pages, 1 figure; to appear, Random Matrices: Theory and Applications. This is the final version, incorporating referee comments