Wrapping Brownian Motion and Heat Kernels. I: Compact Lie Groups

Key Points

• This work aims to explore the relationship between Brownian motion and heat kernels within compact Lie groups.
• Utilized the wrapping map developed by Dooley and Wildberger.
• Studied the heat equation in the context of compact Lie groups.
• Analyzed the fundamental solution of the associated semigroup.
• Successfully demonstrated how to wrap Brownian motion to a compact Lie group from its Lie algebra.
• Identified the heat kernel associated with the wrapped Brownian motion.