On toral eigenfunctions and the random wave model
Jean Bourgain
TL;DR
This paper offers a deterministic approach to modeling the number of nodal domains of eigenfunctions on a 2D torus, integrating recent probabilistic methods with number theory of lattice points.
Contribution
It provides a deterministic implementation of the random wave model for toral eigenfunctions, combining Nazarov and Sodin's work with lattice point arithmetic.
Findings
Deterministic model for nodal domain count on 2D torus
Integration of probabilistic and number-theoretic methods
Enhanced understanding of eigenfunction nodal structures
Abstract
The purpose of this Note is to provide a deterministic implementation of the random wave model for the number of nodal domains in the context of the two-dimensional torus. The approach is based on recent work due to Nazarov and Sodin and arithmetical properties of lattice points on circles.
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Taxonomy
TopicsGeometry and complex manifolds · Quantum chaos and dynamical systems · Mathematical Dynamics and Fractals