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- W2553159917 abstract "It is well known that an $n times n$ 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 $d = Theta ( n^{3} )$. Here we consider this critical window and explicitly compute the total variation distance between the Wishart and GOE matrices when $d / n^{3} to c in (0, infty)$. This shows, in particular, that the phase transition from Wishart to GOE is smooth." @default.
- W2553159917 created "2016-11-30" @default.
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- W2553159917 date "2016-11-17" @default.
- W2553159917 modified "2023-09-27" @default.
- W2553159917 title "A smooth transition from Wishart to GOE" @default.
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