Exponential Waiting Time for a Big Gap in a One-Dimensional Zero-Range Process
Ferrari, P. A. ; Galves, A. ; Landim, C.
Ann. Probab., Tome 22 (1994) no. 4, p. 284-288 / Harvested from Project Euclid
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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.
Publié le : 1994-01-14
Classification:  Zero-range process,  occurrence time of a rare event,  large deviations,  60K35,  82C22,  60F10 
@article{1176988860,
     author = {Ferrari, P. A. and Galves, A. and Landim, C.},
     title = {Exponential Waiting Time for a Big Gap in a One-Dimensional Zero-Range Process},
     journal = {Ann. Probab.},
     volume = {22},
     number = {4},
     year = {1994},
     pages = { 284-288},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176988860}
}

Ferrari, P. A.; Galves, A.; Landim, C. Exponential Waiting Time for a Big Gap in a One-Dimensional Zero-Range Process. Ann. Probab., Tome 22 (1994) no. 4, pp.  284-288. http://gdmltest.u-ga.fr/item/1176988860/