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arXiv · 2609.10358

Periodic ASEP and random walks on affine Hecke Algebra

Alexey Bufetov·Nimisha Pahuja
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Abstract

We study the large time behavior of a periodic ASEP with fixed period started from the step initial condition. We establish the limit shape theorem and the asymptotic distribution of a single second class particle. Our single-species results extend the previous results of Lam and Ayyer-Linusson about periodic TASEP to the ASEP case. These results can also be interpreted as describing the limit behavior of a random walk on affine Hecke algebra.

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Alexey Bufetov, Nimisha Pahuja. 2026-09-09. Periodic ASEP and random walks on affine Hecke Algebra. https://arxiv.org/abs/2609.10358

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