Construction of product $*$-probability spaces via free cumulants

Published 21 Jul 2020 in math.OA, math.CO, and math.PR | (2007.10989v2)

Abstract: It is well known that free independence is equivalent to the vanishing of mixed free cumulants. The purpose of this short note is to build free products of $*$-probability spaces using this as the definition of freeness and relying on free cumulants instead of moments.

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