Limit theorems for random permanents with exchangeable structure

Grzegorz A. Rempala and Jacek Wesolowski

Journal of Multivariate Analysis, 2004, vol. 91, issue 2, 224-239

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.

Keywords: Random; permanent; Orthogonal; expansion; Central; limit; theorem (search for similar items in EconPapers)
Date: 2004
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