Limit theorems for random permanents with exchangeable structure

  • Authors:

  • Grzegorz A. Rempała;Jacek Wesołowski

  • Affiliations:

  • Institute of Mathematics and its Applications (IMA), University of Minnesota, 400 Lind Hall, 207 Church Street S.E., Minneapolis, MN and Department of Mathematics, University of Louisville;Wydział Matematyki i Nauk Informacyjnych Politechnika Warszawska, Warszawa, Poland

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2004

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Abstract

Permanents of random matrices extend the concept of U-statistics with product kernels. In this paper, we study limiting behavior of permanents of random matrices with independent columns of exchangeable components. Our main results provide a general framework which unifies already existing asymptotic theory for projection matrices as well as matrices of all-iid entries. The method of the proofs is based on a Hoeffding-type orthogonal decomposition of a random permanent function. The decomposition allows us to relate asymptotic behavior of permanents to that of elementary symmetric polynomials based on triangular arrays of rowwise independent rv's.