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A Smooth Transition from Wishart to GOE

Author(s): Rácz, Miklos Z; Richey, J

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Abstract: © 2018, Springer Science+Business Media, LLC, part of Springer Nature. It is well known that an n× n Wishart matrix with d degrees of freedom is close to the appropriately centered and scaled Gaussian orthogonal ensemble (GOE) if d is large enough. Recent work of Bubeck, Ding, Eldan, and Racz, and independently Jiang and Li, shows that the transition happens when d= Θ (n 3 ). Here we consider this critical window and explicitly compute the total variation distance between the Wishart and GOE matrices when d/ n 3 → c∈ (0 , ∞). This shows, in particular, that the phase transition from Wishart to GOE is smooth.
Publication Date: 1-Jun-2019
Citation: Rácz, MZ, Richey, J. (2019). A Smooth Transition from Wishart to GOE. Journal of Theoretical Probability, 32 (2), 898 - 906. doi:10.1007/s10959-018-0808-2
DOI: doi:10.1007/s10959-018-0808-2
ISSN: 0894-9840
EISSN: 1572-9230
Pages: 898 - 906
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Theoretical Probability
Version: Author's manuscript

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