Limiting behavior of immanants of certain correlation matrix

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• 作者：Ryo Tabata ^{tabata@ariake-nct.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A15 ; 20C30
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：510
• 期：Complete
• 页码：230-245
• 全文大小：317 K

文摘

A correlation matrix is a positive semi-definite Hermitian matrix with all diagonals equal to 1. The minimum of the permanents on singular correlation matrices is conjectured to be given by the matrix Y_n$Y_n$, all of whose non-diagonal entries are 14ce5a1de30f6551bb4" title="Click to view the MathML source">−1/(n−1)$-1/(n-1)$. Also, Frenzen–Fischer proved that $\mathrm{per}{Y}_n$ approaches to e/2$e/2$ as n→∞$n\to \infty$. In this paper, we analyze some immanants of Y_n$Y_n$, which are the generalizations of the determinant and the permanent, and we generalize these results to some other immanants and conjecture most of those converge to 1.