Entropic Chaos of Mixed Mean-Field Jump Processes

TL;DR

This paper investigates mixed mean-field jump processes, including PDMPs, establishing entropic propagation of chaos and providing explicit bounds on relative entropy between particle systems and their mean-field limits.

Contribution

It introduces a second-order bounded difference condition and proves entropic chaos with explicit bounds, extending the understanding of mean-field jump processes.

Findings

Proves entropic propagation of chaos for mixed mean-field jump processes.

Provides explicit bounds on relative entropy between particle systems and mean-field limits.

Utilizes second-order concentration inequalities for the analysis.

Abstract

This paper studies a class of mixed mean-field jump processes on an abstract state space $\Pi$, together with their associated $N$-particle systems. The dynamics consist of the superposition of an independent Markovian component and a bounded mean-field jump interaction; in particular, piecewise deterministic Markov processes (PDMPs) with mean-field interactions are covered by this framework. Under a second-order bounded difference condition on the mean-field jump kernel, we establish entropic propagation of chaos as $N \to \infty$. In particular, we obtain an explicit qualitative bound on the relative entropy between the law of the $N$-particle system and the product measure induced by the mean-field limit. The proof relies on the second-order concentration inequality introduced in G\"otze and Sambale, 2020.