Abstract
For mean-zero and asymmetric zero-range processes on \({\mathbb{Z}}^{d}\), the fluctuations of additive functionals starting from an invariant measure are considered. Under certain assumptions, we establish when the fluctuations are diffusive and satisfy functional central limit theorems. These results complement those for symmetric zero-range systems and also those for simple exclusion models already in the literature.
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Acknowledgements
The authors thank the enjoyable hospitality of CMAT (Portugal) where the conference “Particle systems and Partial Differential Equations” December 5–7, 2012 took place and part of this work was discussed.
C.B. acknowledges the support of the French Ministry of Education through the grant ANR-10-BLAN 0108 (SHEPI).
P.G. thanks FCT (Portugal) for support through the research project “Non-Equilibrium Statistical Physics” PTDC/MAT/109844/2009. P.G. thanks the Research Centre of Mathematics of the University of Minho, for the financial support provided by “FEDER” through the “Programa Operacional Factores de Competitividade COMPETE” and by FCT through the research project PEst-C/MAT/UI0013/2011.
C.B. and P.G. are grateful to Égide and FCT for the research project FCT/1560/25/1/2012/S.
The research of S.S. was supported in part by NSF DMS-1159026.
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Bernardin, C., Gonçalves, P., Sethuraman, S. (2014). Equilibrium Fluctuations of Additive Functionals of Zero-Range Models. In: Bernardin, C., Gonçalves, P. (eds) From Particle Systems to Partial Differential Equations. Springer Proceedings in Mathematics & Statistics, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54271-8_5
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DOI: https://doi.org/10.1007/978-3-642-54271-8_5
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