Percolation representations of additive particle systems
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917491030097920 |
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| author | Swart, Jan M. |
| author_facet | Swart, Jan M. |
| contents | It is well-known that additive interacting particle systems with a local state space of cardinality two have a percolation representation in terms of open paths in a graphical representation. In this paper, it is shown how such a percolation representation can be constructed more generally when the local state space is a finite distributive lattice. The theory is demonstrated on Krone's two-stage contact process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13371 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Percolation representations of additive particle systems Swart, Jan M. Probability Primary: 82C222, Secondary: 60K35 It is well-known that additive interacting particle systems with a local state space of cardinality two have a percolation representation in terms of open paths in a graphical representation. In this paper, it is shown how such a percolation representation can be constructed more generally when the local state space is a finite distributive lattice. The theory is demonstrated on Krone's two-stage contact process. |
| title | Percolation representations of additive particle systems |
| topic | Probability Primary: 82C222, Secondary: 60K35 |
| url | https://arxiv.org/abs/2605.13371 |