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On the sharpness of a three circles theorem for discrete harmonic functions

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arxiv 1512.03732 v1 pith:563F7R5Y submitted 2015-12-03 math.CA math.APmath.PR

Gabor Lippner , Dan Mangoubi This is my paper · ORCID
classification math.CAmath.APmath.PR
keywords circlesfunctionsharmonictheoremthreediscreteerrorterm
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abstract

Any three circles theorem for discrete harmonic functions must contain an inherent error term. In this paper we find the sharp error term in an $L^2$-three circles theorem for harmonic functions defined in $\Zb^2$. The proof is highly indirect due to combinatorial obstacles and cancellations phenomena. We exploit Newton interpolation methods and recursive arguments.

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  1. A Liouville principle for the random conductance model under degenerate conditions

    math.AP 2019-08 conditional novelty 6.0 of 10

    For stationary ergodic conductances on Z^d with a (p,q)-moment condition and reflection invariance, the space of harmonic functions growing slower than |x|^(1+alpha) has dimension d+1.

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