Abstract
A general condition for a Markov process with finite states is given for the convergence of the normalized hitting time of a rare event to a mean one exponential law. It is then applied to the boundary driven symmetric simple exclusion process for an open set of density profiles which does not contain the stationary density profile.
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Acknowledgements
This problem was formulated to the second author by A. Galves after a talk on nonequilibrium stationary states at NUMEC-USP. The authors would like to thank A. Asselah and E. Scoppola for fruitfull discussions and two anonymous referees whose comments allowed to improve considerably the presentation of this article. The authors acknowledge support from ANR-2010-BLAN-0108-03 SHEPI.
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Dedicated to Herbert Spohn.
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Benois, O., Landim, C. & Mourragui, M. Hitting Times of Rare Events in Markov Chains. J Stat Phys 153, 967–990 (2013). https://doi.org/10.1007/s10955-013-0875-9
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DOI: https://doi.org/10.1007/s10955-013-0875-9