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PreprintCC BY 4.0arXiv

Markov chains arising in the study of random matrices over pro-finite rings

  • Nikita Lvov
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Abstract

Recent work of the author investigates certain random processes, valued in abelian p-groups, that naturally arise in the study of Haar random matrices over ℤp. It was found, somewhat surprisingly, that these processes are reversible Markov chains. In this short note, we give a simple alternative derivation of this fact. The new derivation also proves that this phenomenon is not specific to ℤp, but generalizes to Haar random matrices over any profinite local ring.

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Cite

BibTeXRIS
BibTeX
@misc{lvov2026markov,
  title = {{Markov chains arising in the study of random matrices over pro-finite rings}},
  author = {Nikita Lvov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00134},
  eprint = {2610.00134},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00134},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Markov chains arising in the study of random matrices over pro-finite rings
AU  - Nikita Lvov
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00134
UR  - https://arxiv.org/abs/2610.00134
AB  - Recent work of the author investigates certain random processes, valued in abelian p-groups, that naturally arise in the study of Haar random matrices over ℤ_p. It was found, somewhat surprisingly, that these processes are reversible Markov chains. In this short note, we give a simple alternative derivation of this fact. The new derivation also proves that this phenomenon is not specific to ℤ_p, but generalizes to Haar random matrices over any profinite local ring.
ER  -