A smooth transition from Wishart to GOE
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2016
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| _version_ | 1866909881039060992 |
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| author | Racz, Miklos Z. Richey, Jacob |
| author_facet | Racz, Miklos Z. Richey, Jacob |
| contents | 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 $d = Θ( n^{3} )$. Here we consider this critical window and explicitly compute the total variation distance between the Wishart and GOE matrices when $d / n^{3} \to c \in (0, \infty)$. This shows, in particular, that the phase transition from Wishart to GOE is smooth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1611_05838 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | A smooth transition from Wishart to GOE Racz, Miklos Z. Richey, Jacob Statistics Theory Probability 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 $d = Θ( n^{3} )$. Here we consider this critical window and explicitly compute the total variation distance between the Wishart and GOE matrices when $d / n^{3} \to c \in (0, \infty)$. This shows, in particular, that the phase transition from Wishart to GOE is smooth. |
| title | A smooth transition from Wishart to GOE |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/1611.05838 |