Strong convergence of tensor products of independent G.U.E. matrices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909086619009024 |
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| author | Belinschi, Serban Capitaine, Mireille |
| author_facet | Belinschi, Serban Capitaine, Mireille |
| contents | Given tuples of properly normalized independent $N\times N$ G.U.E. matrices $(X_N^{(1)},\dots,X_N^{(r_1)})$ and $(Y_N^{(1)},\dots,Y_N^{(r_2)})$, we show that the tuple $(X_N^{(1)}\otimes I_N,\dots,X_N^{(r_1)}\otimes I_N,I_N\otimes Y_N^{(1)},\dots,I_N\otimes Y_N^{(r_2)})$ of $N^2\times N^2$ random matrices converges strongly as $N$ tends to infinity. It was shown by Ben Hayes that this result implies that the Peterson-Thom conjecture is true. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_07695 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Strong convergence of tensor products of independent G.U.E. matrices Belinschi, Serban Capitaine, Mireille Operator Algebras Probability Given tuples of properly normalized independent $N\times N$ G.U.E. matrices $(X_N^{(1)},\dots,X_N^{(r_1)})$ and $(Y_N^{(1)},\dots,Y_N^{(r_2)})$, we show that the tuple $(X_N^{(1)}\otimes I_N,\dots,X_N^{(r_1)}\otimes I_N,I_N\otimes Y_N^{(1)},\dots,I_N\otimes Y_N^{(r_2)})$ of $N^2\times N^2$ random matrices converges strongly as $N$ tends to infinity. It was shown by Ben Hayes that this result implies that the Peterson-Thom conjecture is true. |
| title | Strong convergence of tensor products of independent G.U.E. matrices |
| topic | Operator Algebras Probability |
| url | https://arxiv.org/abs/2205.07695 |