2019年10月10日
Matrix models for $\varepsilon$-free independence
Archiv der Mathematik
- 記述言語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s00013-020-01569-7
- 出版者・発行元
- Springer Science and Business Media {LLC}
We investigate tensor products of random matrices, and show that independence of entries leads asymptotically to $\varepsilon$-free independence, a mixture of classical and free independence studied by M{\l}otkowski and by Speicher and Wysoczański. The particular $\varepsilon$ arising is prescribed by the tensor product structure chosen, and conversely, we show that with suitable choices an arbitrary $\varepsilon$ may be realized in this way. As a result we obtain a new proof that $\mathcal{R}^\omega$-embeddability is preserved under graph products of von Neumann algebras, along with an explicit recipe for constructing matrix models.
- リンク情報
- ID情報
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- DOI : 10.1007/s00013-020-01569-7
- ISSN : 0003-889X
- ORCIDのPut Code : 77613794
- arXiv ID : arXiv:1910.04343