Random permanents and symmetric statistics

Borovskikh, Yuri V.; Korolyuk, V. S.

doi:10.1007/bf01002359

Cited by 4 publications

(1 citation statement)

References 8 publications

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“…In the first one, which, due to its natural connection with the theory of U-statistics of infinite order, has been also receiving the most attention, only very special types of matrices A were considered, namely, the so-called finite dimensional projection matrices (i.e., of independent, identically distributed columns and a finite number of independent blocks of identical rows). In this setting, the limiting theory for permanents was considered for instance in [20,25,4,11,21]. In the second, perhaps somewhat more natural setting introduced in the early works of Girko (see e.g., [9, Chapter 2 and 7] and references therein), the limiting theory for random permanents has been concerned simply with the matrices of all independent identically distributed (iid) entries.…”

Section: Article In Pressmentioning

confidence: 99%

Limit theorems for random permanents with exchangeable structure

Rempała¹,

Wesołowski²

2004

Journal of Multivariate Analysis

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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. r 2004 Elsevier Inc. All rights reserved.

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Section: Article In Pressmentioning

confidence: 99%