Cumulants for finite free convolution
Octavio Arizmendi, Daniel Perales
TL;DR
This paper introduces cumulants for finite free convolution, providing a moment-cumulant formula and demonstrating their additive property and convergence to free cumulants as dimension increases.
Contribution
It defines finite free cumulants, establishes their properties, and connects them to free cumulants in the limit, advancing understanding of finite free probability.
Findings
Finite free cumulants are additive under finite free convolution.
These cumulants converge to free cumulants as the dimension tends to infinity.
A moment-cumulant formula for finite free convolution is established.
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.
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