On the largest principal angle between random subspaces

Absil, Pierre-Antoine;Edelman, A;Koev, P
(2006) Linear Algebra and Its Applications — Vol. 414, n° 1, p. 288-294 (2006)

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Abstract
Formulas are derived for the probability density function and the probability distribution function of the largest canonical angle between two p-dirnensional subspaces of R-n chosen from the uniform distribution on the Grassmann manifold (which is the unique distribution invariant by orthogonal transformations of R-n). The formulas involve the gamma function and the hypergeometric function of a matrix argument. (c) 2005 Elsevier Inc. All rights reserved.
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Absil, P.-A., Edelman, A., & Koev, P. (2006). On the largest principal angle between random subspaces. Linear Algebra and Its Applications, 414(1), 288-294. https://doi.org/10.1016/j.laa.2005.10.004 (Original work published 2006)