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On the invariant distribution of a one-dimensional avalanche process. (English) Zbl 1171.60022
The authors consider an interacting particle system derived by an independent family of Poisson processes with rate 1. It is shown that such a process has a unique stationary distribution, which is exponentially mixing and can be simulated. In addition, authors prove that the process tends to equilibrium exponentially fast as time tends to infinity. Finally, it is shown numerically that the invariant distribution of a related mean-field coagulation-fragmentation model is very close to that of the interacting particle system.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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