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On the global fluctuations of block Gaussian matrices
Probability Theory and Related Fields ( IF 2 ) Pub Date : 2019-07-10 , DOI: 10.1007/s00440-019-00925-1 Mario Diaz , James A. Mingo , Serban T. Belinschi
Probability Theory and Related Fields ( IF 2 ) Pub Date : 2019-07-10 , DOI: 10.1007/s00440-019-00925-1 Mario Diaz , James A. Mingo , Serban T. Belinschi
In this paper we study the global fluctuations of block Gaussian matrices within the framework of second-order free probability theory. In order to compute the second-order Cauchy transform of these matrices, we introduce a matricial second-order conditional expectation and compute the matricial second-order Cauchy transform of a certain type of non-commutative random variables. As a by-product, using the linearization technique, we obtain the second-order Cauchy transform of non-commutative rational functions evaluated on selfadjoint Gaussian matrices.
中文翻译:
关于块高斯矩阵的全局涨落
在本文中,我们在二阶自由概率论的框架内研究了块高斯矩阵的全局涨落。为了计算这些矩阵的二阶柯西变换,我们引入了矩阵二阶条件期望并计算了某种类型的非交换随机变量的矩阵二阶柯西变换。作为副产品,使用线性化技术,我们获得了在自伴随高斯矩阵上评估的非交换有理函数的二阶柯西变换。
更新日期:2019-07-10
中文翻译:
关于块高斯矩阵的全局涨落
在本文中,我们在二阶自由概率论的框架内研究了块高斯矩阵的全局涨落。为了计算这些矩阵的二阶柯西变换,我们引入了矩阵二阶条件期望并计算了某种类型的非交换随机变量的矩阵二阶柯西变换。作为副产品,使用线性化技术,我们获得了在自伴随高斯矩阵上评估的非交换有理函数的二阶柯西变换。