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September 2002 Central Limit Theorem for Zero-Range Processes
Hanna Jankowski, Jeremy Quastel, John Sheriff
Methods Appl. Anal. 9(3): 393-406 (September 2002).

Abstract

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.

Citation

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Hanna Jankowski. Jeremy Quastel. John Sheriff. "Central Limit Theorem for Zero-Range Processes." Methods Appl. Anal. 9 (3) 393 - 406, September 2002.

Information

Published: September 2002
First available in Project Euclid: 17 June 2005

zbMATH: 1073.60021
MathSciNet: MR2023132

Rights: Copyright © 2002 International Press of Boston

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Vol.9 • No. 3 • September 2002
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