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Limit theorems for random permanents with exchangeable structure

Author

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  • Rempala, Grzegorz A.
  • Wesolowski, Jacek

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.

Suggested Citation

  • Rempala, Grzegorz A. & Wesolowski, Jacek, 2004. "Limit theorems for random permanents with exchangeable structure," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 224-239, November.
    • Handle: RePEc:eee:jmvana:v:91:y:2004:i:2:p:224-239
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