# A Smooth Transition from Wishart to GOE

## Author(s): Rácz, Miklos Z; Richey, J

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DC FieldValueLanguage
dc.contributor.authorRácz, Miklos Z-
dc.contributor.authorRichey, J-
dc.date.accessioned2021-10-11T14:17:51Z-
dc.date.available2021-10-11T14:17:51Z-
dc.date.issued2019-06-01en_US
dc.identifier.citationRácz, MZ, Richey, J. (2019). A Smooth Transition from Wishart to GOE. Journal of Theoretical Probability, 32 (2), 898 - 906. doi:10.1007/s10959-018-0808-2en_US
dc.identifier.issn0894-9840-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1bp2k-
dc.description.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.en_US
dc.format.extent898 - 906en_US
dc.language.isoen_USen_US
dc.relation.ispartofJournal of Theoretical Probabilityen_US
dc.rightsAuthor's manuscripten_US
dc.titleA Smooth Transition from Wishart to GOEen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1007/s10959-018-0808-2-
dc.identifier.eissn1572-9230-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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