Increasing subsequences and the classical groups.
Rains, E.M. (1998)
The Electronic Journal of Combinatorics [electronic only]
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Rains, E.M. (1998)
The Electronic Journal of Combinatorics [electronic only]
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Diaconis, Persi, Gamburd, Alex (2004)
The Electronic Journal of Combinatorics [electronic only]
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Matsumoto, Sho (2008)
The Electronic Journal of Combinatorics [electronic only]
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Hofmann-Credner, Katrin, Stolz, Michael (2008)
Electronic Communications in Probability [electronic only]
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Jonathan I. Novak (2010)
Banach Center Publications
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We describe an approach to the unitary Weingarten function based on the JM elements of symmetric group algebras. When combined with previously known properties of the Weingarten function, this gives a surprising connection with the Moebius function of the lattice of noncrossing partitions.
Borodin, Alexei (1999)
The Electronic Journal of Combinatorics [electronic only]
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Strahov, E. (2003)
The Electronic Journal of Combinatorics [electronic only]
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Śniady, Piotr (2007)
The Electronic Journal of Combinatorics [electronic only]
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Evans, Steven N. (2002)
Electronic Journal of Probability [electronic only]
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Joseph Najnudel, Ashkan Nikeghbali (2013)
Annales de l’institut Fourier
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In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter ) by replacing the entries equal to one by more general non-vanishing complex random variables. For these ensembles, in contrast with more classical models as the Gaussian Unitary Ensemble, or the Circular Unitary Ensemble, the eigenvalues can be very explicitly computed by using the cycle structure...
Oraby, Tamer F. (2007)
Electronic Communications in Probability [electronic only]
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Tam, Tin-Yau, Yan, Wen (2007)
Applied Mathematics E-Notes [electronic only]
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Vladimirov, Igor, Thompson, Bevan (2006)
Journal of Applied Mathematics and Stochastic Analysis
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König, Wolfgang (2005)
Probability Surveys [electronic only]
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Joel A. Tropp (2008)
Studia Mathematica
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This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original...