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