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Operator-valued Free Multiplicative Convolution: Analytic Subordination Theory and Applications to Random Matrix Theory by Belinschi, Serban T.; Speicher, Roland; Treilhard, John; Vargas, Carlos is a scholarly article available to read on EtoBox.

What is Operator-valued Free Multiplicative Convolution: Analytic Subordination Theory and Applications to Random Matrix Theory about?

We give an explicit description, via analytic subordination, of free multiplicative convolution of operator-valued distributions. In particular, the subordination function is obtained from an iteration process. This algorithm is easily numerically implementable. We present two concrete applications of our method: the product of two free operator-valued semicircular elements and the calculation of the distribution of $dcd+d^2cd^2$ for scalar-valued $c$ and $d$, which are free. Comparision between the solution obtained by our methods and simulations of random matrices shows excellent agreement.

Author

Belinschi, Serban T.; Speicher, Roland; Treilhard, John; Vargas, Carlos

Published

2012

Language

EN