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

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arxiv 2409.03626 v2 pith:ZX27TACV submitted 2024-09-05 math.PR math.GRmath.OAmath.RT

Michael Magee , Mikael de la Salle This is my paper · ORCID
classification math.PRmath.GRmath.OAmath.RT
keywords strongasymptoticfreenesshaarirreduciblepartitionsrepresentationsize
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abstract

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 $n^{\frac{1}{42}-\varepsilon}$ 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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Strongly convergent matrix models for $q$-Gaussian algebras

    math.OA 2026-07 conditional novelty 8.0 of 10

    For |q| < √2−1, q-Gaussian families admit strongly convergent finite random matrix models whose allowed matrix-coefficient dimension exceeds the matrix dimension.

  2. Strong convergence to operator-valued semicirculars

    math.OA 2025-06 accept novelty 8.0 of 10

    This paper proves weak and strong convergence in covariance law for general Gaussian matrix ensembles to operator-valued semicircular families and constructs strongly convergent matrix models for interpolated free gro...

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