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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{bufetov2026periodic,
  title = {{Periodic ASEP and random walks on affine Hecke Algebra}},
  author = {Alexey Bufetov and Nimisha Pahuja},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10358},
  eprint = {2609.10358},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10358},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Periodic ASEP and random walks on affine Hecke Algebra
AU  - Alexey Bufetov
AU  - Nimisha Pahuja
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10358
UR  - https://arxiv.org/abs/2609.10358
AB  - 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.
ER  -