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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.|
|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|
|Pages:||898 - 906|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Journal of Theoretical Probability|
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