Eigenfunctions and Random Waves in the Benjamini-Schramm limit

Miklos Abert; Nicolas Bergeron; Etienne Le Masson

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arXiv · 1810.05601

Eigenfunctions and Random Waves in the Benjamini-Schramm limit

Miklos Abert·Nicolas Bergeron·Etienne Le Masson

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Abstract

We investigate the asymptotic behavior of eigenfunctions of the Laplacian on Riemannian manifolds. We show that Benjamini-Schramm convergence provides a unified language for the level and eigenvalue aspects of the theory. As a result, we present a mathematically precise formulation of Berry's conjecture for a compact negatively curved manifold and formulate a Berry-type conjecture for sequences of locally symmetric spaces. We prove some weak versions of these conjectures. Using ergodic theory, we also analyze the connections of these conjectures to Quantum Unique Ergodicity.

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BibTeX RIS

Miklos Abert, Nicolas Bergeron, Etienne Le Masson. 2018-10-12. Eigenfunctions and Random Waves in the Benjamini-Schramm limit. https://arxiv.org/abs/1810.05601

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