Cutoff profile of ASEP on a segment
Abstract
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 totalvariation cutoff window of ASEP is $N^{1/3}$ and the cutoff profile is $1F_{\mathrm{GUE}},$ where $F_{\mathrm{GUE}}$ is the TracyWidom distribution function. This also gives a new proof of the cutoff itself, shown earlier by Labbé and Lacoin. Our proof combines coupling arguments, the result of TracyWidom about fluctuations of ASEP started from the step initial condition, and exact algebraic identities coming from interpreting the multispecies ASEP as a random walk on a Hecke algebra.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.14924
 arXiv:
 arXiv:2012.14924
 Bibcode:
 2020arXiv201214924B
 Keywords:

 Mathematics  Probability;
 Computer Science  Discrete Mathematics;
 Mathematical Physics
 EPrint:
 22 pages, 3 Figures. V2: Corollary 1 has been given a proof. Several smaller corrections following comments of referees