The Annals of Probability

Exponential Waiting Time for a Big Gap in a One-Dimensional Zero-Range Process

P. A. Ferrari, A. Galves, and C. Landim

Full-text: Open access

Abstract

The first time that the $N$ sites to the right of the origin become empty in a one-dimensional zero-range process is shown to converge exponentially fast, as $N \rightarrow \infty$, to the exponential distribution, when divided by its mean. The initial distribution of the process is assumed to be one of the extremal invariant measures $\nu_\rho, \rho \in (0, 1)$, with density $\rho/(1 - \rho)$. The proof is based on the classical Burke theorem.

Article information

Source
Ann. Probab., Volume 22, Number 1 (1994), 284-288.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988860

Digital Object Identifier
doi:10.1214/aop/1176988860

Mathematical Reviews number (MathSciNet)
MR1258878

Zentralblatt MATH identifier
0793.60108

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35] 60F10: Large deviations

Keywords
Zero-range process occurrence time of a rare event large deviations

Citation

Ferrari, P. A.; Galves, A.; Landim, C. Exponential Waiting Time for a Big Gap in a One-Dimensional Zero-Range Process. Ann. Probab. 22 (1994), no. 1, 284--288. doi:10.1214/aop/1176988860. https://projecteuclid.org/euclid.aop/1176988860


Export citation