Quantum ergodicity for Eisenstein series on hyperbolic surfaces of large genus
Loading...
Access rights
openAccess
CC BY
CC BY
publishedVersion
URL
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Authors
Date
Major/Subject
Mcode
Degree programme
Language
en
Pages
54
Series
Mathematische Annalen, Volume 389, issue 1, pp. 845–898
Abstract
We give a quantitative estimate for the quantum mean absolute deviation on hyperbolic surfaces of finite area 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. Depending on the particular sequence of surfaces considered this gives a result of delocalisation of most cusp forms or of Eisenstein series.Description
Other note
Citation
Masson, E L & Sahlsten, T 2024, 'Quantum ergodicity for Eisenstein series on hyperbolic surfaces of large genus', Mathematische Annalen, vol. 389, no. 1, pp. 845–898. https://doi.org/10.1007/s00208-023-02671-1