2020/09/08 by Steinerberger, Stefan
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2009.03869
Let μ be a compactly supported probability measure on the real line. Bercovici-Voiculescu and Nica-Speicher proved the existence of a free convolution power μ\boxplus k for any real k ≥ 1. The purpose of this short note is to give an elementary description of μ\boxplus k in terms of of polynomials and roots of their derivatives. This bridge allows us to switch back and forth between free probability and the asymptotic behavior of polynomials.