Percolation representations of additive particle systems

TL;DR

This paper extends the percolation representation of additive particle systems from binary states to finite distributive lattices, illustrating the theory with Krone's two-stage contact process.

Contribution

It generalizes the percolation representation to systems with finite distributive lattice states, broadening the applicability of graphical methods.

Findings

Percolation representation can be constructed for systems with finite distributive lattice states.

The theory is demonstrated specifically on Krone's two-stage contact process.

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.