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Limit profiles of ASEP
David A. Henriquez Bernal, Peter Nejjar · 2025-12-17 · via math.PR updates on arXiv.org

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.

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