Rigidity of harmonic functions on the supercritical percolation cluster
arxiv(2023)
摘要
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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关键词
harmonic functions,cluster,rigidity
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