Open Access
January, 1994 Exponential Waiting Time for a Big Gap in a One-Dimensional Zero-Range Process
P. A. Ferrari, A. Galves, C. Landim
Ann. Probab. 22(1): 284-288 (January, 1994). DOI: 10.1214/aop/1176988860


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.


Download Citation

P. A. Ferrari. A. Galves. C. Landim. "Exponential Waiting Time for a Big Gap in a One-Dimensional Zero-Range Process." Ann. Probab. 22 (1) 284 - 288, January, 1994.


Published: January, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0793.60108
MathSciNet: MR1258878
Digital Object Identifier: 10.1214/aop/1176988860

Primary: 60K35
Secondary: 60F10 , 82C22

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

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.22 • No. 1 • January, 1994
Back to Top