Article Dans Une Revue Geometric And Functional Analysis Année : 2026

Strong asymptotic freeness of Haar unitaries in quasi-exponential dimensional representations

Résumé

We prove almost sure strong asymptotic freeness of i.i.d. random unitaries with the following law: sample a Haar unitary matrix of dimension $n$ and then send this unitary into an irreducible representation of $U(n)$. The strong convergence holds as long as the irreducible representation arises from a pair of partitions of total size at most $n^{\frac{1}{24}-\varepsilon}$ and is uniform in this regime. Previously this was known for partitions of total size up to $\asymp\log n/\log\log n$ by a result of Bordenave and Collins.

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hal-04726591 , version 1 (08-10-2024)

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Michael Magee, Mikael de la Salle. Strong asymptotic freeness of Haar unitaries in quasi-exponential dimensional representations. Geometric And Functional Analysis, 2026, ⟨10.1007/s00039-026-00730-8⟩. ⟨hal-04726591⟩
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