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

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


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