Density fluctuations for a zero-range process on the percolation cluster

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 $\mathcal{ S}'(\mathbb {R}^d)$.M.J. was supported by the Belgian Interuniversity Attraction Poles Program P6/02, through the network NOSY ( Nonlinear systems, stochastic processes and statistical mechanics). M.J. would like to thanks the hospitality of Universidade do Minho, where part of this work was done. P. G. express her gratitude to "Fundacao para a Ciencia e Tecnologia" for the financial support with the grant /SFRH/BPD/39991/2007 and to "Fundacao Calouste Gulbenkian" for the Prize "Estimulo a Investigacao" for the research project "Hydrodynamic limit of particle systems". P. G. wants to thank the hospitality of the Universite Catholique de Louvain-la-Neuve and IMPA, where part of this work was done