A large-scale analogue of Zelditch's quantum mixing theorem is established for compact hyperbolic surfaces using the wave equation and geodesic flow mixing, valid for arithmetic and Weil-Petersson random surfaces.
The limit points of the bass notes of arithmetic hyperbolic surfaces.arXiv preprint arXiv:2403.00928
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We prove that the limit points of the bass notes of arithmetic hyperbolic surfaces are the interval $\left[0,\frac{1}{4}\right]$.
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math.SP 2representative citing papers
A survey of recent results proving that random hyperbolic surfaces of large genus have near-optimal spectral gaps, after Hide–Magee, Anantharaman–Monk, and Hide–Macera–Thomas.
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Quantum Mixing and Benjamini-Schramm Convergence of Hyperbolic Surfaces
A large-scale analogue of Zelditch's quantum mixing theorem is established for compact hyperbolic surfaces using the wave equation and geodesic flow mixing, valid for arithmetic and Weil-Petersson random surfaces.
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Bass notes of random hyperbolic surfaces of large genus
A survey of recent results proving that random hyperbolic surfaces of large genus have near-optimal spectral gaps, after Hide–Magee, Anantharaman–Monk, and Hide–Macera–Thomas.