Corpus ID: 220128030

Quantum ergodicity for Eisenstein series on hyperbolic surfaces of large genus

@article{Masson2020QuantumEF,
  title={Quantum ergodicity for Eisenstein series on hyperbolic surfaces of large genus},
  author={E. Masson and Tuomas Sahlsten},
  journal={arXiv: Spectral Theory},
  year={2020}
}
We give a quantitative estimate for the quantum variance on hyperbolic surfaces in terms of geometric parameters such as the genus, number of cusps and injectivity radius. It implies a delocalisation result of quantum ergodicity type for eigenfunctions of the Laplacian on hyperbolic surfaces of finite area that Benjamini-Schramm converge to the hyperbolic plane. We show that this is generic for Mirzakhani's model of random surfaces chosen uniformly with respect to the Weil-Petersson volume… Expand

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