Density fluctuations for a zero-range process on the percolation cluster. (English) Zbl 1189.60174

Gonçalves, Patrícia C.; Jara, Milton D.

Electron. Commun. Probab. 14, 382-395 (2009).

Summary: We prove that the density fluctuations for a zero-range process evolving on the \(d\)-dimensional supercritical percolation cluster, with \(d\geq 3\), are given by a generalized Ornstein-Uhlenbeck process in the space of distributions \(\mathcal S'(\mathbb{R}^d)\).

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60G20	Generalized stochastic processes

Keywords:

percolation cluster; zero-range process; density fluctuations