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.
On the spectral gap of negatively curved surface covers.Interna- tional Mathematics Research Notices, 2025(24):rnaf357,
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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.