Second order cumulants: Second order even elements and $R$-diagonal elements

IF 1.5 Q2 PHYSICS, MATHEMATICAL
Octavio Arizmendi, James A. Mingo
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引用次数: 1

Abstract

We introduce $R$-diagonal and even operators of second order. We give a formula for the second order free cumulants of the square $x^2$ of a second order even element in terms of the second order free cumulants of $x$. Similar formulas are proved for the second order free cumulants of $aa^\*$, when $a$ is a second order $R$-diagonal operator. We also show that if $r$ is second order $R$-diagonal and $b$ is second order free from $r$, then $rb$ is also second order $R$-diagonal. We present a large number of examples, in particular, the limit distribution of products of Ginibre matrices. We prove the conjectured formula of Dartois and Forrester for the fluctuations moments of the product of two independent complex Wishart matrices and generalize it to any number of factors.
二阶累积量:二阶偶元素和R -对角元素
引入了二阶R -对角线算子和偶算子。给出了二阶偶元的平方x^2的二阶自由累积量用x的二阶自由累积量表示的公式。对于$aa^\*$的二阶自由累积量,当$a$是二阶$R$-对角算子时,证明了类似的公式。我们还证明了如果$r$是二阶$r$ -对角线$b$是二阶不受$r$影响的,那么$rb$也是二阶$r$ -对角线。我们给出了大量的例子,特别是Ginibre矩阵乘积的极限分布。我们证明了两个独立的复Wishart矩阵乘积的波动矩的Dartois和Forrester的猜想公式,并将其推广到任意数目的因子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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