Abstract
An improvement of the Liouville theorem for discrete harmonic functions on is obtained. More precisely, we prove that there exists a positive constant ε such that if u is discrete harmonic on and for each sufficiently large square Q centered at the origin on a portion of Q, then u is constant.
Dedication
To Fedya Nazarov with admiration
Citation
Lev Buhovsky. Alexander Logunov. Eugenia Malinnikova. Mikhail Sodin. "A discrete harmonic function bounded on a large portion of is constant." Duke Math. J. 171 (6) 1349 - 1378, 15 April 2022. https://doi.org/10.1215/00127094-2021-0037
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