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We show that the stationary measure for the totally asymmetric simple exclusion process on a segment with open boundaries is given by a marginal of a two-line measure with a simple and explicit description. We use this representation to analyze asymptotic fluctuations of the height function near the triple point for a larger set of parameters than was previously studied. As a second application, we determine a single expression for the rate function in the large deviation principle for the height function in the fan and in the shock region. We then discuss how this expression relates to the expressions available in the literature.
Bryc et al. (Tue,) studied this question.