Minimal growth harmonic functions on lamplighter groups

Itai Benjamini, Hugo Duminil-Copin, Gady Kozma, Ariel Yadin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study the minimal possible growth of harmonic functions on lamplighters. We find that (Z/2) (Formula presented.) Z2 has no sublinear harmonic functions, (Z/2) (Formula presented.) Z2 has no sublogarithmic harmonic functions, and neither has the repeated wreath product (… (Z/2 (Formula presented.) Z2) (Formula presented.) Z2) (Formula presented.) … (Symbol found) Z2. These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem.

Original languageEnglish
Pages (from-to)833-858
Number of pages26
JournalNew York Journal of Mathematics
StatePublished - 16 Jul 2017


  • Entropy
  • Harmonic functions
  • Kaimanovich-Vershik
  • Lamplighter
  • Random walk
  • Wreath product

ASJC Scopus subject areas

  • General Mathematics


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