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Central limit theorem for a class of linear systems. (English) Zbl 1189.60181
Summary: We consider a class of interacting particle systems with values in [\(0,\infty )^{\mathbb{Z}^{d}}\), of which the binary contact path process is an example. For d \(\geq 3\) and under a certain square integrability condition on the total number of the particles, we prove a central limit theorem for the density of the particles, together with upper bounds for the density of the most populated site and the replica overlap.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F05 Central limit and other weak theorems
60J25 Continuous-time Markov processes on general state spaces
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