Key points are not available for this paper at this time.
We use ideas from quantitative homogenization to show that nonconstant harmonic functions on the percolation cluster cannot satisfy certain structural constraints, for example, a Lipschitz bound.These unique-continuation-type results are false on the full lattice and hence the disorder is utilized in an essential way.
Bou‐Rabee et al. (Fri,) studied this question.