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SUMMARY:Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic
  surfaces - Etienne Le Masson (Bristol)
DTSTART:20170228T163000Z
DTEND:20170228T173000Z
UID:TALK70619@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:The quantum ergodicity theorem states that on compact hyperbol
 ic surfaces\, most eigenfunctions of the Laplacian equidistribute spatiall
 y in the large eigenvalue limit. We will present an alternative equidistri
 bution theorem for eigenfunctions where the eigenvalues stay bounded and w
 e take instead sequences of compact hyperbolic surfaces converging to the 
 plane in the sense of Benjamini and Schramm. This approach is motivated by
  joint works with Anantharaman\, Brooks and Lindenstrauss on eigenvectors 
 of the discrete Laplacian on regular graphs. The proof uses an ergodic the
 orem of Nevo.\nJoint work with Tuomas Sahlsten.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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