Integrals over Grassmannians and Random permutations

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dc.creatorAdler, M.
dc.creatorvan Moerbeke, P.
dc.date2001-10-25
dc.date.accessioned2026-07-07T04:44:05Z
dc.date.available2026-07-07T04:44:05Z
dc.descriptionIn testing the independence of two Gaussian populations, one computes the distribution of the sample canonical correlation coefficients, given that the actual correlation is zero. The "Laplace transform" of this distribution is not only an integral over the Grassmannian of p-dimensional planes in complex n-space, but is also related to a generalized hypergeometric function. Such integrals are solutions of Painlevé-like equations. They also have expansions, related to random words of length l formed with an alphabet of p letters. Given that each letter appears in the word, the maximal length of the disjoint union of p increasing subsequences of the word clearly equals l. But the maximal length of the disjoint union of p-1 increasing subsequences leads to a non-trivial distribution. It is precisely this probability which appears in the expansion above.
dc.description68 pages
dc.identifierhttps://arxiv.org/abs/math/0110281
dc.identifierhttp://arxiv.org/abs/math/0110281
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62494
dc.subjectCombinatorics
dc.subjectMathematical Physics
dc.subjectProbability
dc.subjectExactly Solvable and Integrable Systems
dc.titleIntegrals over Grassmannians and Random permutations
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