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.
Bibliographical noteFunding 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.
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