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Askey-Wilson signed measures and open ASEP in the shock region

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arxiv 2307.06574 v3 pith:WTLS2EHZ submitted 2023-07-13 math.PR

Yizao Wang , Jacek Wesolowski , Zongrui Yang This is my paper · ORCID
classification math.PR
keywords asepaskey-wilsondensitymeasuresopensigneddescriptionprofile
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We introduce a family of multi-dimensional Askey-Wilson signed measures. We offer an explicit description of the stationary measure of the open asymmetric simple exclusion process (ASEP) in the full phase diagram, in terms of integrations with respect to these Askey-Wilson signed measures. Using our description, we provide a rigorous derivation of the density profile and limit fluctuations of open ASEP in the entire shock region, including the high and low density phases as well as the coexistence line. This in particular confirms the existing physics postulations of the density profile.

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  1. Free Askey--Wilson functionals and geometric last passage percolation on a strip

    math.PR 2025-06 conditional novelty 6.0 of 10

    Free Askey-Wilson functionals yield generating function representations for geometric LPP on a strip, giving the full phase diagram of the stationary measure and a Poisson approximation.

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