Furstenberg entropy realizations for virtually free groups and lamplighter groups

Yair Hartman*, Omer Tamuz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Let (G,µ) be a discrete group with a generating probability measure. Nevo showed that if G has Kazhdan’s property (T), then there exists ɛ > 0 such that the Furstenberg entropy of any (G,µ)-stationary ergodic space is either 0 or larger than ɛ. Virtually free groups, such as SL2(ℤ), do not have property (T), and neither do their extensions, such as surface groups. For virtually free groups, we construct stationary actions with arbitrarily small, positive entropy. The construction involves building and lifting spaces of lamplighter groups. For some classical lamplighter gropus, these spaces realize a dense set of entropies between 0 and the Poisson boundary entropy.

Original languageEnglish (US)
Pages (from-to)227-257
Number of pages31
JournalJournal d'Analyse Mathematique
Volume126
Issue number1
DOIs
StatePublished - Apr 20 2015

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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