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Eigenfunctions and Random Waves in the Benjamini-Schramm limit. (arXiv:1810.05601v1 [math.SP])
来源于:arXiv
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. 查看全文>>