Limit profiles of ASEP

We study the asymmetric simple exclusion process (ASEP) on a segment ${1,\ldots,b_N}$ and are interested in its total variation distance to equilibrium when started from an initial configuration $ξ^{N}$. We provide a general result which gives the cutoff window and profile whenever a KPZ-type limit theorem is available for an extension of $ξ^{N}$ 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.

💡 Research Summary

The paper investigates the mixing behavior of the asymmetric simple exclusion process (ASEP) on a finite segment, focusing on the total variation (TV) distance between the law of the process started from a fixed initial configuration ξ_N and its stationary distribution π_{b_N,a_N,k_N}. While previous work (notably