Cumulants of a convolution and applications to monotone probability theory

TL;DR

This paper explores the properties of cumulants within convolution operations and their applications to monotone probability theory, providing foundational insights into non-commutative probability structures.

Contribution

It introduces new cumulant techniques for convolution in monotone probability, advancing the understanding of non-commutative independence.

Findings

Derived formulas for monotone cumulants

Established connections between cumulants and convolution operations

Applied cumulant theory to monotone independence scenarios

Abstract

The contents are divided into two papers "The Monotone Cumulants" (arXiv:0907.4896) and "Conditionally monotone independence" (arXiv:0907.5473).