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Large deviations for the asymmetric simple exclusion process. (English) Zbl 1114.60026

Funaki, Tadahisa (ed.) et al., Stochastic analysis on large scale interacting systems. Papers from the 11th international conference, Hayama, Japan, July 17–26, 2002 and the international conference on stochastic analysis and statistical mechanics, Kyoto, Japan, July 29–30, 2002. Tokyo: Mathematical Society of Japan (ISBN 4-931469-24-8/hbk). Advanced Studies in Pure Mathematics 39, 1-27 (2004).
The paper is a presentation of the work carried out by Leif Jensen in his PhD dissertation on large deviations of totally asymmetric simple exclusion process (TASEP), presented at NYU in the year 2000. It explains the large deviation behavior (validity of the hydrodynamic scaling) for the TASEP in one dimension. So far, large deviations from hydrodynamic scaling have been worked out only for systems under diffusive scaling. A detailed sketch is presented of the derivation of the upper bound on the asymptotics of a specific entropy function, together with a rough outline of how the lower bound is established.
For the entire collection see [Zbl 1050.60001].

MSC:

60F10 Large deviations
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
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