Speaker: Yuxi Han (Purdue University)

Title: Large deviations and Hamilton–Jacobi Equations for state-constrained chemical reactions

Abstract: Chemical reactions can be modeled as random time-changed Poisson processes on a countable state space. Their macroscopic behavior, including large fluctuations, can be analyzed through the WKB reformulation. In this framework, the backward equation of the rescaled process leads to a discrete Hamilton–Jacobi equation with state constraints. As the grid size tends to zero, the limiting solution and its variational representation are closely related to the good rate function in the large deviation principle for state-constrained chemical reactions in the thermodynamic limit. In this talk, we will examine the limiting behavior of discrete Hamilton–Jacobi equations with state-constraint boundary conditions and establish the corresponding large deviation principle. This is joint work with Yuan Gao.