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math.AP2023
Unique continuation on planar graphs
Ahmed Bou-Rabee, William Cooperman, Shirshendu Ganguly
We show that a discrete harmonic function which is bounded on a large portion of a periodic planar graph is constant. A key ingredient is a new unique continuation result for the w…
math.PR2023
Rigidity of harmonic functions on the supercritical percolation cluster
Ahmed Bou-Rabee, William Cooperman, Paul Dario
We use ideas from quantitative homogenization to show that nonconstant harmonic functions on the percolation cluster cannot satisfy certain structural constraints, for example, a L…