Vertex-Face/Zeta correspondence

Komatsu, Takashi; Konno, Norio; Sato, Iwao

doi:10.1007/s10801-022-01122-5

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2022

2024

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Cited by 6 publications

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“…Furthermore, a relation between the IPS and zeta function is called IPS/Zeta Correspondence, and it is introduced in Komatsu, Konno, and Sato [6]. The zeta correspondence is studied for various other models [5,3,4,7]. In particular, Walk/Zeta Correspondence [5] is based on the one-particle system in the lattice space; on the other hand, our focus is on the multi-particle system in the configuration space.…”

Section: Introductionmentioning

confidence: 99%

IPS/Zeta Correspondence for the Domany-Kinzel model

Kiumi¹,

Konno²,

Oshima³

2022

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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.

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