Principal angles between random subspaces and polynomials in two free projections
Confluentes Mathematici, Volume 13 (2021) no. 2, pp. 3-10.

We use the geometric concept of principal angles between subspaces to compute the noncommutative distribution of an expression involving two free projections. For example, this allows to simplify a formula by Fevrier–Mastnak–Nica–Szpojankowski about the free Bernoulli anticommutator. As a byproduct, we observe the remarkable fact that the principal angles between random half-dimensional subspaces are asymptotically distributed according to the uniform measure on [0,π/2].

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DOI: 10.5802/cml.74
Classification: 46L54
Keywords: free probability, principal angles, random subspace
Guillaume Aubrun 1

1 Université de Lyon; CNRS; Université Lyon 1; Institut Camille Jordan UMR5208, 69622 Villeurbanne Cedex, France
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Guillaume Aubrun. Principal angles between random subspaces and polynomials in two free projections. Confluentes Mathematici, Volume 13 (2021) no. 2, pp. 3-10. doi : 10.5802/cml.74. https://cml.centre-mersenne.org/articles/10.5802/cml.74/

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