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This short note explains how to use ready-to-use components of symbolic software to convert between the free cumulants and the moments of measures without sophisticated programming. This allows quick access to low order moments of free convolutions of measures, which can be used to test whether a given probability measure is a free convolution of other… (More)

This paper presents two simple formulas for approximation of the standard normal right tail probabilities, and indicates the method of computing approximations of higher order. One of the approximations relies on two simple numerical constants, has absolute error of 0.00071 and relative error 0.023; the other uses four numerical constants, has absolute… (More)

In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. This paper proposes a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. While it considers random matrices, it takes an operator-valued free probability approach to… (More)

In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. We propose a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. We will also calculate the asymptotic eigenvalue distribution of HH * , where the entries of H are jointly… (More)

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