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Benoit Collins

  1. Integration of invariant matrices and application to statistics.

    Пнд, 05/07/2012 - 15:01 — SomNambul
    Authors: Benoit Collins, Sho Matsumoto, Nadia Saad
    Subjects: Statistics
    Abstract

    We consider random matrices that have invariance properties under the action
    of unitary groups (either a left-right invariance, or a conjugacy invariance),
    and we give formulas for moments in terms of functions of eigenvalues. Our main
    tool is the Weingarten calculus. As an application to statistics, we obtain new
    formulas for the pseudo inverse of Gaussian matrices and for the inverse of
    compound Wishart matrices.

  2. Asymptotic fluctuations of representations of the unitary groups.

    Втр, 12/01/2009 - 16:01 — SomNambul
    Authors: Benoit Collins, Piotr Sniady
    Subjects: Representation Theory
    Abstract

    We study asymptotics of representations of the unitary groups U(n) in the
    limit n\to\infty and we show that in many aspects they behave like large random
    matrices. In particular, we show that the highest weight of a random
    irreducible component in the Kronecker tensor product of two irreducible
    representations behaves asymptotically in the same way as the spectrum of the
    sum of two large random matrices with prescribed eigenvalues.

  3. On polynomial integrals over the orthogonal group.

    Чт, 10/08/2009 - 10:54 — SomNambul
    Authors: Jean-Marc Schlenker, Teodor Banica, Benoit Collins
    Subjects: Mathematical Physics
    Abstract

    We consider integrals of type $\int_{O_n}u_{11}^{a_1}...
    u_{1n}^{a_n}u_{21}^{b_1}... u_{2n}^{b_n} du$, with respect to the Haar measure
    on the orthogonal group. We establish several remarkable invariance properties
    satisfied by such integrals, by using combinatorial methods. We present as well
    a general formula for such integrals, as a sum of products of factorials.

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