Cutoff on Ramanujan complexes and classical groups

Michael Chapman, Ori Parzanchevski

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The total-variation cutoff phenomenon has been conjectured to hold for simple random walk on all transitive expanders. However, very little is actually known regarding this conjecture, and cutoff on sparse graphs in general. In this paper we establish total-variation cutoff for simple random walk on Ramanujan complexes of type Azd (d 1). As a result, we obtain explicit generators for the finite classical groups PGLn.Fq/ for which the associated Cayley graphs exhibit total-variation cutoff.

Original languageAmerican English
Pages (from-to)431-456
Number of pages26
JournalCommentarii Mathematici Helvetici
Issue number3
StatePublished - 2022

Bibliographical note

Funding Information:
Acknowledgements. The authors are grateful to Ori Gurel-Gurevich for his help with proving Proposition 4.2. They also thank Eyal Lubetzky, Alex Lubotzky and Nati Linial for helpful discussions and encouragement. M.C. was supported by ERC grant 339096 of Nati Linial and by ERC, BSF and NSF grants of Alex Lubotzky. O.P. was supported by ISF grant 2990/21.

Publisher Copyright:
© 2022 European Mathematical Society Publishing House. All rights reserved.


  • Bruhat–Tits buildings
  • Cutoff
  • Ramanujan complexes
  • expanders
  • random walks


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