Strong Asymptotic Freeness of Haar Unitaries in Quasi-Exponential Dimensional Representations
Abstract
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 $n$ n and then send this unitary into an irreducible representation of $\mathrm{U}(n)$ U ( n ) . The strong convergence holds as long as the irreducible representation arises from a pair of partitions of total size at most $n^{\frac{1}{42}-\varepsilon }$ n 1 42 − ε and is uniform in this regime. Previously this was known for partitions of total size up to $\asymp \log n/\log \log n$ ≍ log n / log log n by a result of Bordenave and Collins.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
advanced mathematical theories
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Geometric and Functional Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 36
- Issue
- 1
- Pages
- 152–200
- Publication date
- 1 February 2026
- Language
- EN