Matrix liberation process III: Unitary Brownian motion and martingale analysis

TL;DR

This paper studies large deviation rate functions for matrix liberation processes driven by unitary Brownian motion, using a martingale problem approach to analyze the stochastic structure.

Contribution

It introduces a novel free martingale problem formulation for analyzing matrix liberation processes driven by unitary Brownian motion.

Findings

Derived rate functions for large deviations in matrix liberation processes

Formulated and solved a free martingale problem framework

Provides new insights into the stochastic structure of the process

Abstract

We investigate the rate functions that emerge in our previous works towards large deviation principle for the matrix liberation process driven by the unitary Brownian motion as well as the unitary Brownian motion itself. Our approach is grounded in the viewpoint of the martingale problem. Specifically, we formulate and solve a "free martingale problem" within this framework, which provides a new perspective on the underlying stochastic structure.