Stochastic Calculus and Hochschild Homology

TL;DR

This paper explores the connection between probabilistic methods in topological quantum mechanics and Hochschild homology, proposing a new perspective on topological correlations through large variance limits.

Contribution

It introduces a probabilistic approach to homological aspects of topological quantum field theory, linking topological correlations with Hochschild homology.

Findings

Probabilistic topological correlations relate to Hochschild homology.

Large variance limits provide a new framework for topological correlations.

Illustrates the relation between circle-based correlations and Hochschild homology.

Abstract

This paper is a case study of probabilistic approach to homological aspects of topological quantum field theory via the example of topological quantum mechanics. We propose topological correlations in terms of large variance limit. An investigation on the relation between probabilistic topological correlations on the circle and Hochschild homology is illustrated.