Central Limit Theorem for Zero-Range Processes
Quastel, Jeremy ; Jankowski, Hanna ; Sheriff, John
Methods Appl. Anal., Tome 9 (2002) no. 3, p. 393-406 / Harvested from Project Euclid
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We consider additive functionals INTt-0 V(ns )ds of symmetric zero-range processes, where V is a mean zero local function. In dimensions 1 and 2 we obtain a central limit theorem for a-1(t) INTt-0 V(ns)ds with a(t) = SQRROOT (tlogt) in d =2 and a(t) = t 3/4 in d = 1 and an explicit form for the asymptotic variance SIGMA2. The transient case d greater than or equal to 3 can be handled by standard arguments [KV, SX,S]. We also obtain corresponding invariance principles. This generalizes results obtained by Port (see [CG]) for noninteracting random walks and Kipnis [K] for the symmetric simple exclusion process. Our main tools are the martingale method together with L2 decay estimates [JLQY] for the process semigroup.
Publié le : 2002-09-14
Classification:  
@article{1119027731,
     author = {Quastel, Jeremy and Jankowski, Hanna and Sheriff, John},
     title = {Central Limit Theorem for Zero-Range Processes},
     journal = {Methods Appl. Anal.},
     volume = {9},
     number = {3},
     year = {2002},
     pages = { 393-406},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1119027731}
}

Quastel, Jeremy; Jankowski, Hanna; Sheriff, John. Central Limit Theorem for Zero-Range Processes. Methods Appl. Anal., Tome 9 (2002) no. 3, pp.  393-406. http://gdmltest.u-ga.fr/item/1119027731/