Divergence and quasi-isometry classes of random Gromov's monsters

Dominik Gruber, Alessandro Sisto

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We show that Gromov's monsters arising from i.i.d. random labellings of expanders (that we call random Gromov's monsters) have linear divergence along a subsequence, so that in particular they do not contain Morse quasigeodesics, and they are not quasi-isometric to Gromov's monsters arising from graphical small cancellation labellings of expanders. Moreover, by further studying the divergence function, we show that there are uncountably many quasi-isometry classes of random Gromov's monsters.

Original languageEnglish
JournalMathematical Proceedings of the Cambridge Philosophical Society
Early online date18 Feb 2021
Publication statusE-pub ahead of print - 18 Feb 2021


  • 2020 Mathematics Subject Classification:
  • 20F65

ASJC Scopus subject areas

  • Mathematics(all)


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