Abstract
Cyclic monotone independence is an algebraic notion of non-commutative 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 independence with an appropriately chosen state. This observation provides a unified nonrandom matrix model for both types of monotone independences.
Funding Statement
BC was partially supported by JSPS Kakenhi 17H04823, 20K20882, 21H00987, JPJSBP120203202. FL was supported by the SFB-TRR 195’Symbolic Tools in Mathematics and their Application’ of the German Research Foundation (DFG). NS was partially supported by JSPS Kakenhi 19H01791, 19K03515, JPJSBP120209921, JPJSBP120203202.
Acknowledgments
We are grateful to Roland Speicher and Takahiro Hasebe for preliminary comments on our preprint and useful discussions, and to Akihiro Miyagawa for a careful reading. We would also like to thank two anonymous referees for their very careful reading of our manuscript, and multiple suggestions of improvement.
Citation
Benoît Collins. Felix Leid. Noriyoshi Sakuma. "Matrix models for cyclic monotone and monotone independences." Electron. Commun. Probab. 29 1 - 14, 2024. https://doi.org/10.1214/24-ECP622
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