Cumulants for finite free convolution

2016/11/20 by Arizmendi, Octavio, Perales, Daniel · 5 citations
#05A18 #46L54 #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1611.06598

Abstract

In this paper we define cumulants for finite free convolution. We give a moment-cumulant formula and show that these cumulants satisfy desired properties: they are additive with respect to finite free convolution and they approach free cumulants as the dimension goes to infinity.

Cited by

• Finite free probability and S transforms of Jacobi processes
• Crystallization of discrete N-particle systems at high temperature
• Finite N precursors of the free cumulants
• Critical points of random polynomials and finite free cumulants
• Infinitesimal freeness for orthogonally invariant random matrices

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