Algebraic Central Limit Theorems: A Personal View on One of Wilhelm's Legacies -- To the Memory of Wilhelm von Waldenfels

TL;DR

This paper explores the algebraic central limit theorem for quantum random variables, emphasizing its mathematical significance and personal reflection on Wilhelm von Waldenfels's influence.

Contribution

It introduces the algebraic central limit theorem for quantum variables, extending classical convergence concepts into the quantum domain with a personal perspective.

Findings

Extension of classical convergence in moments to quantum variables

Development of algebraic central limit theorem for quantum random variables

Personal insights into mathematical research inspired by Wilhelm von Waldenfels

Abstract

Bringing forward the concept of convergence in moments from classical random variables to quantum random variables is what leads to what can be called algebraic central limit theorem for (classical and) quantum random variables. I reflect in a very personal way how such an idea is typical for the spirit of doing research in mathematics as I learned it in Wilhelm von Waldenfels's research group in Heidelberg.