Quantum Ergodicity and Averaging Operators on the Sphere

Shimon Brooks, Etienne Le Masson, Elon Lindenstrauss*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We prove quantum ergodicity for certain orthonormal bases of L2(S2), consisting of joint eigenfunctions of the Laplacian on S2 and the discrete averaging operator over a finite set of rotations, generating a free group. If, in addition, the rotations are algebraic, we give a quantified version of this result. The methods used also give a new, simplified proof of quantum ergodicity for large regular graphs.

Original languageAmerican English
Pages (from-to)6034-6064
Number of pages31
JournalInternational Mathematics Research Notices
Issue number19
StatePublished - 2016

Bibliographical note

Funding Information:
E.L. and E.L.M. were supported by ERC AdG grant no. 267259. S.B. was supported by NSF grant DMS-1101596, ISF grant 1119/13, and a Marie-Curie Career Integration Grant. This paper was finalized while both E.L. and E.L.M. were in residence at MSRI, supported in part by NSF grant no. 0932078-000.

Publisher Copyright:
© 2015 The Author(s). Published by Oxford University Press. All rights reserved.


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