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We study the number of nodal domains in balls shrinking slightly above the Planck scale for "generic" toral eigenfunctions. We prove that, up to the natural scaling, the nodal domains… Click to show full abstract
We study the number of nodal domains in balls shrinking slightly above the Planck scale for "generic" toral eigenfunctions. We prove that, up to the natural scaling, the nodal domains count obeys the same asymptotic law as the global number of nodal domains. The proof, on one hand, uses new arithmetic information to refine Bourgain's de-randomisation technique at Planck scale. And on the other hand, it requires a Planck scale version of Yau's conjecture which we believe to be of independent interest.
Keywords:
toral eigenfunctions;
nodal domains;
planck scale;
scale number;
number nodal
Journal Title: Journal of Functional Analysis
Year Published: 2020
Link to full text (if available)
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Journal Title: Journal of Functional Analysis
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!