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Strong convergence for tensor GUE random matrices

By Wangjun Yuan

Appears in collection : Jean Morlet Chair - Research school: Random quantum channels: entanglement and entropies / Chaire Jean Morlet - Ecole: Canaux quantiques aléatoires: Intrication et entropies

Haagerup and Thorbjørnsen proved that iid GUEs converge strongly to free semicircular elements as the dimension grows to infinity. Motivated by considerations from quantum physics -- in particular, understanding nearest neighbor interactions in quantum spin systems -- we consider iid GUE acting on multipartite state spaces, with a mixing component on two sites and identity on the remaining sites. We show that under proper assumptions on the dimension of the sites, strong asymptotic freeness still holds. Our proof relies on an interpolation technology recently introduced by Bandeidra, Boedihardjo and van Handel. This is a joint work with Benoît Collins.

Information about the video

Date of recording 08/07/2024
Date of publication 26/07/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20200603
Cite this video Yuan, Wangjun (08/07/2024). Strong convergence for tensor GUE random matrices. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20200603
URL https://dx.doi.org/10.24350/CIRM.V.20200603

Domain(s)

Bibliography

BANDEIRA, Afonso S., BOEDIHARDJO, March T., et VAN HANDEL, Ramon. Matrix concentration inequalities and free probability. Inventiones mathematicae, 2023, vol. 234, no 1, p. 419-487. - https://doi.org/10.1007/s00222-023-01204-6
HAAGERUP, Uffe et THORBJØRNSEN, Steen. A new application of random matrices: $\text{Ext}(C_{\text{red}}^{\ast}(F_{2}))$ is not a group. Annals of Mathematics, 2005, p. 711-775. - https://www.jstor.org/stable/20159928

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