For the fan region of open ASEP, the stationary height profile satisfies an LDP with rate function depending only on the two boundary effective densities, equal to the open TASEP rate function.
Stationary Distribution of open Asymmetric Simple Exclusion Processes on an Interval as a marginal of a two-layer ensemble
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abstract
We investigate the asymmetric simple exclusion process (ASEP) on an interval with open boundaries. We provide a representation for its stationary distribution as a marginal of the top layer of a two-layer ensemble under Liggett's condition. The representation is valid in the fan region and in the shock region, extending the representation previously obtained in [Bryc-Zatitskii-2024 arXiv:2403.03275] to ASEP. We also give a recursion for the two-layer weight function.
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Large deviation principle for the stationary measures of open asymmetric simple exclusion processes
For the fan region of open ASEP, the stationary height profile satisfies an LDP with rate function depending only on the two boundary effective densities, equal to the open TASEP rate function.