Quantum ergodicity and averaging operators on the sphere

Shimon Brooks, Etienne Le Masson, Elon Lindenstrauss

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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 languageEnglish
JournalInternational Mathematics Research Notices
Publication statusPublished - 24 Nov 2015


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