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PreprintarXiv licencearXiv

Cutoff for the Adjacent Transposition Shuffle on a Cycle

  • Colin Defant
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Abstract

In the adjacent transposition shuffle on a cycle, n distinct cards are placed at the vertices of a cycle, and adjacent cards swap positions according to independent Poisson clocks of rate 1. We prove that this Markov chain exhibits total variation cutoff at time n2log n/(8π2), with a window of order at most n2loglog n.

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Cite

BibTeXRIS
BibTeX
@misc{defant2026cutoff,
  title = {{Cutoff for the Adjacent Transposition Shuffle on a Cycle}},
  author = {Colin Defant},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.40076},
  eprint = {2609.40076},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.40076},
}
RIS
TY  - UNPB
TI  - Cutoff for the Adjacent Transposition Shuffle on a Cycle
AU  - Colin Defant
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.40076
UR  - https://arxiv.org/abs/2609.40076
AB  - In the adjacent transposition shuffle on a cycle, n distinct cards are placed at the vertices of a cycle, and adjacent cards swap positions according to independent Poisson clocks of rate 1. We prove that this Markov chain exhibits total variation cutoff at time n^2log n/(8π^2), with a window of order at most n^2loglog n.
ER  -