Lamplighter graphs do not admit harmonic functions of finite energy

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.

References in corpus (1)

• On the spectrum of lamplighter groups and percolation clusters

Cited by in corpus (2)

• Mixing, malnormal subgroups and cohomology in degree one
• Minimal growth harmonic functions on lamplighter groups