Cutoff profile of ASEP on a segment

Abstract This paper studies the mixing behavior of Asymmetric Simple Exclusion Process (ASEP) on a segment length N . Our main result is that for particle densities in (0, 1), total-variation cutoff window ASEP $$N^{1/3}$$ N 1 / 3 and profile $$1-F_{\mathrm {GUE}},$$ - F GUE , where $$F_{\mathrm {GUE}}$$ Tracy-Widom distribution function. also gives new proof itself, shown earlier by Labbé Lacoin. combines coupling arguments, Tracy–Widom about fluctuations started from step initial condition, exact algebraic identities coming interpreting multi-species as random walk Hecke algebra.