Wrapping Brownian motion and heat kernels II: symmetric spaces

TL;DR

This paper extends previous work on wrapping Brownian motion and heat kernels from compact Lie groups to symmetric spaces, including complex and non-compact cases, with generalizations of key formulas and functions.

Contribution

It introduces a global generalization of Rouvière's formula and the $e$-function for symmetric spaces, expanding the scope of heat kernel analysis.

Findings

Extended wrapping results to various symmetric spaces.

Generalized Rouvière's formula and $e$-function.

Included complex and non-compact symmetric spaces.

Abstract

In this paper we extend our previous results on wrapping Brownian motion and heat kernels onto compact Lie groups to various symmetric spaces, where a global generalisation of Rouvi\`ere's formula and the $e$-function are considered. Additionally, we extend some of our results to complex Lie groups, and certain non-compact symmetric spaces.