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Stationary Distribution of open Asymmetric Simple Exclusion Processes on an Interval as a marginal of a two-layer ensemble

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arxiv 2408.06535 v3 pith:64BGCPON submitted 2024-08-12 math.PR math-phmath.MP

Wlodek Bryc This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords representationtwo-layerasepasymmetricdistributionensembleexclusioninterval
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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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  1. Large deviation principle for the stationary measures of open asymmetric simple exclusion processes

    math.PR 2024-12 accept novelty 7.0 of 10

    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.

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