Homotopy Probability Theory II

TL;DR

This paper extends homotopy probability theory by developing a deformation framework that replaces vector spaces with chain complexes, integrating derived mathematics into classical and noncommutative probability.

Contribution

It introduces a deformation theoretic framework for homotopy probability theory, enabling the use of chain complexes of random variables and derived mathematics principles.

Findings

Framework facilitates the development of homotopy probability theory.

Example demonstrates application of the framework.

Links homotopy algebra with probability theory.

Abstract

This is the second of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. This paper outlines how the framework can assist in the development of homotopy probability theory, where a vector space of random variables is replaced by a chain complex of random variables. This allows the principles of derived mathematics to participate in classical and noncommutative probability theory. A simple example is presented.