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arXiv · 2303.04736

Rigidity of harmonic functions on the supercritical percolation cluster

Ahmed Bou-Rabee·William Cooperman·Paul Dario
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Abstract

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.

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Ahmed Bou-Rabee, William Cooperman, Paul Dario. 2023-03-08. Rigidity of harmonic functions on the supercritical percolation cluster. https://arxiv.org/abs/2303.04736

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