| Título: | Existence of multi-dimensional infinite volume self-organized critical forest-fire models |
| Autores: | Maximilian, Duerre; Mathematisches Institut der Université München |
| Fecha: | 2006-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
forest-fires; self-organized criticality; forest-fire model; existence; well-defined Primary 60K35; 82C20; 82C22 |
| Descripción: | Consider the following forest-fire model where the possible locations of trees are the sites of a cubic lattice. Each site has two possible states: 'vacant' or 'occupied'. Vacant sites become occupied according to independent rate 1 Poisson processes. Independently, at each site ignition (by lightning) occurs according to independent rate lambda Poisson processes. When a site is ignited, its occupied cluster becomes vacant instantaneously. If the lattice is one-dimensional or finite, then with probability one, at each time the state of a given site only depends on finitely many Poisson events; a process with the above description can be constructed in a standard way. If the lattice is infinite and multi-dimensional, in principle, the state of a given site can be influenced by infinitely many Poisson events in finite time. |
| Idioma: | No aplica |
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