Lamplighter graphs do not admit harmonic functions of finite energy

2009/07/08 by Agelos Georgakopoulos, Georgakopoulos, Agelos
Mathematics · Physics and Astronomy · #05C25 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Group Theory (math.GR) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.CO #math.GR #msc:05C25

paper · pdf · doi:10.48550/arxiv.0907.1398

openalex publication_date 2009/07/08 · arxiv created 2009/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a lamplighter graph of a locally finite graph over a finite graph does not admit a non-constant harmonic function of finite Dirichlet energy.

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