IPS/Zeta Correspondence for the Domany-Kinzel model

TL;DR

This paper investigates the zeta function for a class of interacting particle systems, including the Domany-Kinzel model, extending previous work on one-particle and multi-particle models with probabilistic or quantum interactions.

Contribution

It introduces the IPS/Zeta correspondence specifically for the Domany-Kinzel model, expanding the understanding of zeta functions in complex probabilistic interacting systems.

Findings

Established the zeta function for the Domany-Kinzel model

Extended the IPS/Zeta correspondence to multi-particle probabilistic models

Connected zeta functions with statistical mechanics and biological models

Abstract

Previous studies presented zeta functions by the Konno-Sato theorem or the Fourier analysis for one-particle models, including random walks, correlated random walks, quantum walks, and open quantum random walks. Furthermore, the zeta functions for the multi-particle model with probabilistic or quantum interactions, called the interacting particle system (IPS), were also investigated. In this paper, we focus on the zeta function for a class of IPS, including the Domany-Kinzel model, which is a typical model of the probabilistic IPS in the field of statistical mechanics and mathematical biology.