Matrix models for cyclic monotone and monotone independences
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915010396028928 |
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| author | Collins, Benoît Leid, Felix Sakuma, Noriyoshi |
| author_facet | Collins, Benoît Leid, Felix Sakuma, Noriyoshi |
| contents | Cyclic monotone independence is an algebraic notion of noncommutative independence, introduced in the study of multi-matrix random matrix models with small rank. Its algebraic form turns out to be surprisingly close to monotone independence, which is why it was named cyclic monotone independence. This paper conceptualizes this notion by showing that the same random matrix model is also a model for the monotone convergence with an appropriately chosen state. This observation provides a unified nonrandom matrix model for both types of monotone independences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_11666 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Matrix models for cyclic monotone and monotone independences Collins, Benoît Leid, Felix Sakuma, Noriyoshi Operator Algebras Probability 60B20, 46L54 Cyclic monotone independence is an algebraic notion of noncommutative independence, introduced in the study of multi-matrix random matrix models with small rank. Its algebraic form turns out to be surprisingly close to monotone independence, which is why it was named cyclic monotone independence. This paper conceptualizes this notion by showing that the same random matrix model is also a model for the monotone convergence with an appropriately chosen state. This observation provides a unified nonrandom matrix model for both types of monotone independences. |
| title | Matrix models for cyclic monotone and monotone independences |
| topic | Operator Algebras Probability 60B20, 46L54 |
| url | https://arxiv.org/abs/2202.11666 |