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arXiv · 2512.14584

Limit profiles of ASEP

David A. Henriquez Bernal·Peter Nejjar
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Abstract

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 $\xi^{N}$. 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.

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David A. Henriquez Bernal, Peter Nejjar. 2025-12-16. Limit profiles of ASEP. https://arxiv.org/abs/2512.14584

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