Abstract
We obtain the fluctuations for the occupation time of one-dimensional symmetric exclusion processes with speed change, where the transition rates (conductances) are driven by a general function \(W\). The approach does not require sharp bounds on the spectral gap of the system nor the jump rates to be bounded from above or below. We present some examples and for one of them, we observe that the fluctuations of the current are trivial, but the fluctuations of the occupation time are given by a fractional Brownian Motion. This shows that, in general, the fluctuations of the current and of the occupation time are not of same order.
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Acknowledgments
The authors thank hospitality to CMAT (Portugal) where this work was initiated, IMPA and PUC (Rio de Janeiro) where it was finished. T.F. was supported through a grant “BOLSISTA DA CAPES - Brasília/Brasil” provided by CAPES (Brazil) and a Project PRODOC-UFBA. A.N. thanks CNPq (Brazil) for support through the research Project “Mecânica estatística fora do equilíbrio para sistemas estocásticos” Universal n. 479514/2011-9. P.G. thanks FCT (Portugal) for support through the research Project “Non - Equilibrium Statistical Physics” PTDC/MAT/109844/2009 and also thanks CNPq (Brazil) for the research Project “Additive functionals of particle systems” Universal n. 480431/2013-2. P.G. was partially supported by the Research Centre of Mathematics of the University of Minho and the Portuguese Funds from “Fundação para a Ciência e a Tecnologia”, through the Project PEstOE/MAT/UI0013/2014.
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Franco, T., Gonçalves, P. & Neumann, A. Occupation Time of Exclusion Processes with Conductances. J Stat Phys 156, 975–997 (2014). https://doi.org/10.1007/s10955-014-1039-2
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DOI: https://doi.org/10.1007/s10955-014-1039-2