The random walk on upper triangular matrices over Z/ mZ

Evita Nestoridi, Allan Sly

Research output: Contribution to journalArticlepeer-review


We study a natural random walk on the n× n uni-upper triangular matrices, with entries in Z/ mZ , generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this random walk is O(m2nlog n+ n2mo(1)) . This answers a question of Stong and of Arias-Castro, Diaconis, and Stanley.

Original languageEnglish (US)
Pages (from-to)571-601
Number of pages31
JournalProbability Theory and Related Fields
Issue number3-4
StatePublished - Dec 2023

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Markov chains
  • Mixing times
  • Upper triangular matrices


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