The fractional free convolution of $R$-diagonal elements and random polynomials under repeated differentiation

Andrew Campbell, Sean O'Rourke, David Renfrew

We extend the free convolution of Brown measures of $R$-diagonal elements introduced by Kösters and Tikhomirov [Probab. Math. Statist. 38 (2018), no. 2, 359--384] to fractional pow…