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arXiv · 1402.2207

Bulk behaviour of Schur-Hadamard products of symmetric random matrices

Arup Bose·Soumendu Sundar Mukherjee
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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.

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Arup Bose, Soumendu Sundar Mukherjee. 2014-02-10. Bulk behaviour of Schur-Hadamard products of symmetric random matrices. https://arxiv.org/abs/1402.2207

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