## Brazilian Journal of Probability and Statistics

### Finite exclusion process and independent random walks

E. D. Andjel

#### Abstract

We show that the total variational distance between a process of two particles interacting by exclusion and a process of two independent particles goes to $0$ as time goes to infinity, when the underlying one particle system is a symmetric random walk on $\mathbb{Z}^{d}$ with finite second moments. Upper bounds for the speed of convergence are given.

#### Article information

Source
Braz. J. Probab. Stat., Volume 27, Number 2 (2013), 227-244.

Dates
First available in Project Euclid: 21 February 2013

https://projecteuclid.org/euclid.bjps/1361455037

Digital Object Identifier
doi:10.1214/11-BJPS170

Mathematical Reviews number (MathSciNet)
MR3028806

Zentralblatt MATH identifier
06365961

Keywords
Exclusion system random walks

#### Citation

Andjel, E. D. Finite exclusion process and independent random walks. Braz. J. Probab. Stat. 27 (2013), no. 2, 227--244. doi:10.1214/11-BJPS170. https://projecteuclid.org/euclid.bjps/1361455037

#### References

• De Masi A. and Presutti E. (1983). Probability estimates for symmetric simple exclusion random walks. Annales de l’Institut Henri Poincaré (B) Probabilités et Statistiques 19, 71–85.
• Ferrari P. A., Presutti E., Scacciatelli E. and Vares M. E. (1991). The symmetric simple exclusion process I Probability estimates. Stochastic Processes and Their Applications 39, 89–105.
• Konno N. (1995). Asymptotic behaviour of basic contact process with rapid stirring. Journal of Theoretical Probability 8, 833–876.
• Liggett T. M. (1985). Interacting Particle Systems. New York: Springer-Verlag.
• Liggett T. M. (1999). Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Berlin: Springer-Verlag.
• Spitzer F. (1976). Principle of Random Walk, 2nd ed. New York: Springer-Verlag.