A simple proof for monotone CLT

TL;DR

This paper provides a straightforward proof of the monotone CLT by leveraging combinatorial structures, addressing a gap in understanding compared to other types of independence.

Contribution

It introduces a simple combinatorial approach using peakless pair partitions to clarify the mechanism behind the monotone CLT.

Findings

Clarified the proof of the monotone CLT

Used combinatorial structures to simplify understanding

Enhanced theoretical understanding of monotone independence

Abstract

In the case of monotone independence, the transparent understanding of the mechanism to validate the central limit theorem (CLT) has been lacking, in sharp contrast to commutative, free and Boolean cases. We have succeeded in clarifying it by making use of simple combinatorial structure of peakless pair partitions.