Truncations of random unitary matrices and Young tableaux

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dc.creatorNovak, Jonathan
dc.date2006-08-03
dc.date2006-08-06
dc.date.accessioned2026-07-07T07:21:23Z
dc.date.available2026-07-07T07:21:23Z
dc.descriptionLet $U$ be a matrix chosen randomly, with respect to Haar measure, from the unitary group $U(d).$ We express the moments of the trace of any submatrix of $U$ as a sum over partitions whose terms count certain standard and semistandard Young tableaux. Using this combinatorial interpretation, we obtain a simple closed form for the moments of an individual entry of a random unitary matrix and use this to deduce that the entries converge in moments to standard complex Gaussian random variables. In addition, we recover a well-known theorem of E. Rains which shows that the moments of the trace of a random unitary matrix enumerate permutations with restricted increasing subsequence length.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0608108
dc.identifierhttp://arxiv.org/abs/math/0608108
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115284
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.titleTruncations of random unitary matrices and Young tableaux
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