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On Hadamard powers of random Wishart matrices

Baslingker, J (2023) On Hadamard powers of random Wishart matrices. In: Electronic Communications in Probability, 28 .

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Official URL: https://doi.org/10.1214/23-ECP561


A famous result of Horn and Fitzgerald is that the β-th Hadamard power of any n � n positive semi-definite (p.s.d.) matrix with non-negative entries is p.s.d. for all β � n�2 and is not necessarily p.s.d. for β < n � 2, with β /� N. In this article, we study this question for random Wishart matrix An:= XnXTn, where Xn is n � n matrix with i.i.d. Gaussian entries. It is shown that applying x � |x|α entrywise to An, the resulting matrix is p.s.d., with high probability, for α > 1 and is not p.s.d., with high probability, for α < 1. It is also shown that if Xn are (Formula Presented) matrices, for any s < 1, then the transition of positivity occurs at the exponent α = s. © 2023, Institute of Mathematical Statistics. All rights reserved.

Item Type: Journal Article
Publication: Electronic Communications in Probability
Publisher: Institute of Mathematical Statistics
Additional Information: The copyright for this article belongs to author
Department/Centre: Others
Date Deposited: 04 Mar 2024 10:19
Last Modified: 04 Mar 2024 10:19
URI: https://eprints.iisc.ac.in/id/eprint/84063

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