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 Î²th Hadamard power of any n Ã� n positive semidefinite (p.s.d.) matrix with nonnegative entries is p.s.d. for all Î² â�¥ nâ��2 and is not necessarily p.s.d. for Î² < n â�� 2, with Î² /â�� N. In this article, we study this question for random Wishart matrix An:= XnXTn, where Xn is n Ã� n matrix with i.i.d. Gaussian entries. It is shown that applying x â�� xÎ± entrywise to An, the resulting matrix is p.s.d., with high probability, for Î± > 1 and is not p.s.d., with high probability, for Î± < 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 Î± = s. Â© 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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