Stationary Measures and Mean Flux Depending on Multiple Conserved Quantities in a Stochastic Cellular Automaton
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917552264839168 |
|---|---|
| author | Endo, Kazushige Iwao, Shinsuke Nagai, Hidetomo Nakano, Yushi |
| author_facet | Endo, Kazushige Iwao, Shinsuke Nagai, Hidetomo Nakano, Yushi |
| contents | We analyze a stochastic 5-neighbor cellular automaton with several conserved quantities, including the particle density. By examining the eigenvalue problem of the associated transition matrix, we derive an explicit formula for the stationary distribution on each irreducible component, in which the weight of each configuration is expressed in terms of the numbers of occurrences of two specific local patterns. This analysis further allows us to theoretically derive the dependence of the mean flux on the conserved quantities. In particular, we recover the mean flux formula in the deterministic case by taking the zero-noise limit of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28052 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stationary Measures and Mean Flux Depending on Multiple Conserved Quantities in a Stochastic Cellular Automaton Endo, Kazushige Iwao, Shinsuke Nagai, Hidetomo Nakano, Yushi Mathematical Physics Probability Cellular Automata and Lattice Gases 37B15, 60J10, 60K35, 82C70 We analyze a stochastic 5-neighbor cellular automaton with several conserved quantities, including the particle density. By examining the eigenvalue problem of the associated transition matrix, we derive an explicit formula for the stationary distribution on each irreducible component, in which the weight of each configuration is expressed in terms of the numbers of occurrences of two specific local patterns. This analysis further allows us to theoretically derive the dependence of the mean flux on the conserved quantities. In particular, we recover the mean flux formula in the deterministic case by taking the zero-noise limit of the system. |
| title | Stationary Measures and Mean Flux Depending on Multiple Conserved Quantities in a Stochastic Cellular Automaton |
| topic | Mathematical Physics Probability Cellular Automata and Lattice Gases 37B15, 60J10, 60K35, 82C70 |
| url | https://arxiv.org/abs/2605.28052 |