Large Deviation Principle for the Whittaker 2d Growth Model

TL;DR

This paper establishes a large deviation principle for the Whittaker 2d growth model, a complex Markov diffusion process, by developing a novel rate function and addressing challenges from spatiotemporal interactions.

Contribution

It introduces the first large deviation principle for the Whittaker 2d growth model, utilizing Schider's Theorem and a new approach for intersecting paths.

Findings

Established a large deviation principle for the model

Developed a novel rate function for the process

Addressed complexities from path intersections

Abstract

The Whittaker 2d growth model is a triangular continuous Markov diffusion process that appears in many scientific contexts. It has been theoretically intriguing to establish a large deviation principle for this 2d process with a scaling factor. The main challenge is the spatiotemporal interactions and dynamics that may depend on potential sample-path intersections. We develop such a principle with a novel rate function. Our approach is mainly based on Schider's Theorem, contraction principle, and special treatment for intersecting sample paths.