Existence of a stationary distribution for multi-dimensional infinite volume forest-fire processes

Alice Stahl (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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 Z^d, 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 Z^d, d>=2.

Mots clés: forest-fire process

Domaines: Probabilités [math.PR]

Alice Stahl. Existence of a stationary distribution for multi-dimensional infinite volume forest-fire processes. 2012. ⟨hal-00682397⟩