Reflection positive affine actions and stochastic processes

TL;DR

This paper explores the relationship between reflection positivity, affine isometric actions on Hilbert spaces, and Gaussian processes with stationary increments, advancing the understanding of their interconnected representation theoretic aspects.

Contribution

It clarifies the connections between reflection positivity, affine actions, and Gaussian processes, providing new insights into their representation theoretic framework.

Findings

Established links between reflection positivity and affine isometric actions

Connected reflection positivity with Gaussian processes with stationary increments

Enhanced understanding of the representation theoretic aspects of these concepts

Abstract

In this note we continue our investigations of the representation theoretic aspects of reflection positivity, also called Osterwalder--Schrader positivity. We explain how this concept relates to affine isometric actions on real Hilbert spaces and how this is connected with Gaussian processes with stationary increments.