For stationary ergodic conductances on Z^d with a (p,q)-moment condition and reflection invariance, the space of harmonic functions growing slower than |x|^(1+alpha) has dimension d+1.
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A Liouville principle for the random conductance model under degenerate conditions
For stationary ergodic conductances on Z^d with a (p,q)-moment condition and reflection invariance, the space of harmonic functions growing slower than |x|^(1+alpha) has dimension d+1.