GNS mixing-time conjecture for asymmetric exclusion in the maximal current phase

Consider the asymmetric simple exclusion process on a segment of size $N$ with open boundaries, in which particles have a drift, may move in both directions within the segment, and may enter and exit at both endpoints. In the maximal current phase, the mixing time is the time required for this process to approach its stationary distribution. GNS mixing-time conjecture. The mixing time is of order $N^{3/2}$, and the cutoff phenomenon does not occur. This is an open problem attributed in the source to GNS:MixingOpen; the corresponding assertion for the totally asymmetric process is established in the setting studied in the paper.