# 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}
}
• Published 29 December 2020
• Mathematics
• Probability Theory and Related Fields
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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