On the invariant distribution of a one-dimensional avalanche process
Bressaud, Xavier ; Fournier, Nicolas
Ann. Probab., Tome 37 (2009) no. 1, p. 48-77 / Harvested from Project Euclid
We consider an interacting particle system (ηt)t≥0 with values in {0, 1}, in which each vacant site becomes occupied with rate 1, while each connected component of occupied sites become vacant with rate equal to its size. We show that such a process admits a unique invariant distribution, which is exponentially mixing and can be perfectly simulated. We also prove that for any initial condition, the avalanche process tends to equilibrium exponentially fast, as time increases to infinity. Finally, we consider a related mean-field coagulation–fragmentation model, we compute its invariant distribution and we show numerically that it is very close to that of the interacting particle system.
Publié le : 2009-01-15
Classification:  Stochastic interacting particle systems,  equilibrium,  coalescence,  fragmentation,  self-organized criticality,  forest-fire model,  60K35
@article{1234881684,
     author = {Bressaud, Xavier and Fournier, Nicolas},
     title = {On the invariant distribution of a one-dimensional avalanche process},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 48-77},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1234881684}
}
Bressaud, Xavier; Fournier, Nicolas. On the invariant distribution of a one-dimensional avalanche process. Ann. Probab., Tome 37 (2009) no. 1, pp.  48-77. http://gdmltest.u-ga.fr/item/1234881684/