Quantum ergodicity and Benjamini–Schramm convergence of hyperbolic surfaces

@article{Masson2017QuantumEA,
  title={Quantum ergodicity and Benjamini–Schramm convergence of hyperbolic surfaces},
  author={Etienne Le Masson and Tuomas Sahlsten},
  journal={Duke Mathematical Journal},
  year={2017},
  volume={166},
  pages={3425-3460}
}
We present a quantum ergodicity theorem for fixed spectral window and sequences of compact hyperbolic surfaces converging to the hyperbolic plane in the sense of Benjamini and Schramm. This addresses a question posed by Colin de Verdiere. Our theorem is inspired by results for eigenfunctions on large regular graphs by Anantharaman and the first-named author. It applies in particular to eigenfunctions on compact arithmetic surfaces in the level aspect, which connects it to a question of Nelson… Expand

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