Electronic Communications in Probability

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

Patricia Goncalves and Milton Jara

Full-text: Open access

Abstract

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 $\mathscr{S}'(\mathbb{R}^d)$.

Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 38, 382-395.

Dates
Accepted: 8 September 2009
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234747

Digital Object Identifier
doi:10.1214/ECP.v14-1491

Mathematical Reviews number (MathSciNet)
MR2545289

Zentralblatt MATH identifier
1189.60174

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
percolation cluster zero-range process density fluctuations

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Goncalves, Patricia; Jara, Milton. Density fluctuations for a zero-range process on the percolation cluster. Electron. Commun. Probab. 14 (2009), paper no. 38, 382--395. doi:10.1214/ECP.v14-1491. https://projecteuclid.org/euclid.ecp/1465234747


Export citation

References

  • Andjel, Enrique Daniel. Invariant measures for the zero range processes. Ann. Probab. 10 (1982), no. 3, 525–547.
  • Antal, Peter; Pisztora, Agoston. On the chemical distance for supercritical Bernoulli percolation. Ann. Probab. 24 (1996), no. 2, 1036–1048.
  • Berger, Noam; Biskup, Marek. Quenched invariance principle for simple random walk on percolation clusters. Probab. Theory Related Fields 137 (2007), no. 1-2, 83–120.
  • Chang, Chih Chung. Equilibrium fluctuations of gradient reversible particle systems. Probab. Theory Related Fields 100 (1994), no. 3, 269–283.
  • Faggionato, Alessandra. Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit. Electron. J. Probab. 13 (2008), 2217–2247.
  • Gonçalves, Patrícia; Jara, Milton. Scaling limits for gradient systems in random environment. J. Stat. Phys. 131 (2008), no. 4, 691–716.
  • bibitem Geoffrey Grimmett. Percolation, volume 321 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, second edition, 1999. \1707339
  • Holley, Richard A.; Stroock, Daniel W. Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions. Publ. Res. Inst. Math. Sci. 14 (1978), no. 3, 741–788.
  • bibitem Claude Kipnis and Claudio Landim. Scaling limits of interacting particle systems, volume 320 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1999. \1707314
  • Mathieu, P.; Piatnitski, A. Quenched invariance principles for random walks on percolation clusters. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 463 (2007), no. 2085, 2287–2307.
  • Sidoravicius, Vladas; Sznitman, Alain-Sol. Quenched invariance principles for walks on clusters of percolation or among random conductances. Probab. Theory Related Fields 129 (2004), no. 2, 219–244.
  • Tartar, L. Homogénéisation et compacité par compensation.(French) Séminaire Goulaouic-Schwartz (1978/1979), Exp. No. 9, 9 pp., École Polytech., Palaiseau, 1979.