PreprintarXiv licencearXiv
Percolation representations of additive particle systems
Abstract
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.
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BibTeX
@misc{swart2026percolation,
title = {{Percolation representations of additive particle systems}},
author = {Jan M. Swart},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.13371},
eprint = {2605.13371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.13371},
}
RIS
TY - UNPB
TI - Percolation representations of additive particle systems
AU - Jan M. Swart
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2605.13371
UR - https://arxiv.org/abs/2605.13371
AB - 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.
ER -