Limit theorems for random permanents with exchangeable structure |
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Authors: | Grzegorz A Rempa
a Jacek Weso
owski |
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Institution: | a Institute of Mathematics and its Applications (IMA), University of Minnesota, Minneapolis, MN 55455-0436, USA;b Department of Mathematics, University of Louisville, USA;c Wydzia
Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warszawa, Poland |
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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. |
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Keywords: | Random permanent Orthogonal expansion Central limit theorem |
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