Convergence of the open WASEP stationary measure without Liggett’s condition

Abstract

We demonstrate that Liggett’s condition can be relaxed without disrupting the convergence of open ASEP stationary measures to the open KPZ stationary measure. This is equivalent to demonstrating that, under weak asymmetry scaling and appropriate scaling of time and space, the four-parameter Askey–Wilson process converges to a two-parameter continuous dual Hahn process. We conjecture that the convergence of the open ASEP height function process to solutions to the open KPZ equation will hold for a wider range of ASEP parameters than those permitted by Liggett’s condition.