  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.
