Limit profiles of ASEP

We study the asymmetric simple exclusion process (ASEP) on a segment $\{1,\dots ,b_N\}$ and are interested in its total variation distance to equilibrium when started from an initial configuration ${\xi }^N$. We provide a general result which gives the cutoff window and profile whenever a KPZ-type limit theorem is available for an extension of ${\xi }^N$ to $\mathbb{Z}$. We apply this result to obtain the cutoff window and profile of ASEP on the segment with flat, half-flat and step initial data. Our arguments are entirely probabilistic and make no use of Hecke algebras.