Bose, Arup ; Mukherjee, Soumendu Sundar (2014) Bulk behavior of Schur–Hadamard products of symmetric random matrices Random Matrices: Theory and Applications, 03 (02). p. 1450007. ISSN 2010-3263
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Official URL: http://doi.org/10.1142/S2010326314500075
Related URL: http://dx.doi.org/10.1142/S2010326314500075
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 LSD 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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to World Scientific Publishing Co Pte Ltd. |
| ID Code: | 135048 |
| Deposited On: | 18 Jan 2023 08:51 |
| Last Modified: | 18 Jan 2023 08:51 |
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