Existence of a stationary distribution for multi-dimensional infinite volume forest-fire processes
Abstract
Consider the following forest-fire process on a connected graph. Each site of the graph can be either occupied or vacant. A vacant site becomes occupied with rate 1. A site is ignited with rate lambda, and its whole occupied cluster burns instantaneously. The purpose of this paper is to show the existence of a stationary distribution for forest-fire processes on Zd, for d >= 2. We define a distribution as a limit of a sequence of invariant distributions of finite volume forest-fire processes, and then show it is a stationary distribution for forest-fire processes on Zd, d>=2.
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