Cutoff profile of ASEP on a segment

@article{Bufetov2022CutoffPO,
  title={Cutoff profile of ASEP on a segment},
  author={Alexey Bufetov and Peter Nejjar},
  journal={Probability Theory and Related Fields},
  year={2022},
  pages={1-25}
}
This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length N . Our main result is that for particle densities in (0, 1),  the total-variation cutoff window of ASEP is $$N^{1/3}$$ N 1 / 3 and the cutoff profile is $$1-F_{\mathrm {GUE}},$$ 1 - F GUE , where $$F_{\mathrm {GUE}}$$ F GUE is the Tracy-Widom distribution function. This also gives a new proof of the cutoff itself, shown earlier by Labbé and Lacoin. Our proof combines coupling… 
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