We introduce the Askey-Wilson signed measures as a new tool for studying the stationary measure of the open asymmetric simple exclusion process (ASEP). As applications of this technique, we derive several asymptotic properties of open ASEP: the density profile, limit fluctuations, the open KPZ fixed-point limit, the half-line ASEP limit, large deviations, and open ASEP with light particles. Based on joint works with Zhipeng Liu, Dominik Schmid, Yizao Wang and Jacek Wesolowski.
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