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  1. ; ; (, International Mathematics Research Notices)
    Abstract We extend the free convolution of Brown measures of $$R$$-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions. 
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  2. ; (, Proceedings of the American Mathematical Society)
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