2021/09/14 by Guillaume Aubrun, Aubrun, Guillaume · 1 citation
Computer Science · Mathematics · #46L54 #Advanced Algebra and Geometry #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications
paper · doi:10.48550/arxiv.2109.06535
openalex publication_date 2021/09/14 · openalex created_date 2022/08/25 · openalex updated_date 2026/07/28
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. We also derive economically an explicit formula for the free additive convolution of Bernoulli distributions. 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.