Wiener distribution on holonomy groups

TL;DR

This paper establishes a convergence theorem for Wiener measures on holonomy groups, using stochastic parallel transport along converging metric connections, advancing understanding of probabilistic structures in geometric analysis.

Contribution

It introduces a new convergence theorem for Wiener measures on holonomy groups based on stochastic parallel transport and metric connection convergence.

Findings

Proves convergence of Wiener measures on holonomy groups.

Links stochastic parallel transport with measure convergence.

Provides a theoretical foundation for probabilistic geometric analysis.

Abstract

This paper proves a convergence theorem for the push-forward Wiener measures on holonomy groups via stochastic parallel transports along convergent metric connections.