Shock fluctuations for the Hammersley process. (English) Zbl 1364.82039
Summary: We consider the Hammersley interacting particle system starting from a shock initial profile with densities \(\rho ,\lambda \in {\mathbb R}\) \((\rho < \lambda)\). The microscopic shock is taken as the position of a second-class particle initially at the origin, and the main results are: (i) a central limit theorem for the shock; (ii) the variance of the shock equals \(2[\lambda \rho (\lambda - \rho )]^{-1}t + O(t^{2/3})\). By using the same method of proof, we also prove similar results for first-class particles.
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 60F05 | Central limit and other weak theorems |
| 60J75 | Jump processes (MSC2010) |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
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