Quantitative equidistribution properties of toral eigenfunctions

DOI10.4171/JST/169zbMath1369.58022arXiv1503.02794MaRDI QIDQ2361001

Gabriel Rivière, Hamid Hezari

Publication date: 29 June 2017

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.02794

zbMATH Keywords

eigenfunctions of the Laplacianquantum ergodicityWeyl lawBirkhoff theorem

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51) Harmonic analysis and PDEs (42B37)

Related Items (17)

Distribution of the nodal sets of eigenfunctions on analytic manifolds ⋮ Equidistribution in shrinking sets and \(L^4\)-norm bounds for automorphic forms ⋮ Planck-scale mass equidistribution of toral Laplace eigenfunctions ⋮ Equidistribution of toral eigenfunctions along hypersurfaces ⋮ Quadratic forms and semiclassical eigenfunction hypothesis for flat tori ⋮ Small scale equidistribution for a point scatterer on the torus ⋮ Equidistribution of random waves on small balls ⋮ Looping directions and integrals of eigenfunctions over submanifolds ⋮ Quantitative equidistribution of eigenfunctions for toral Schrödinger operators ⋮ Applications of small-scale quantum ergodicity in nodal sets ⋮ \(L^{p}\) norms, nodal sets, and quantum ergodicity ⋮ CENTRAL LIMIT THEOREM FOR PLANCK‐SCALE MASS DISTRIBUTION OF TORAL LAPLACE EIGENFUNCTIONS ⋮ Quantum ergodicity and \(L^{p}\) norms of restrictions of eigenfunctions ⋮ Small scale equidistribution of random eigenbases ⋮ Eigenstate thermalization hypothesis for Wigner matrices ⋮ Small scale equidistribution of eigenfunctions on the torus ⋮ Planck-scale distribution of nodal length of arithmetic random waves

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