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SUMMARY:Quantum chaos on discrete graphs - Smilansky\, U (Weizmann Institu
 te)
DTSTART:20081217T140000Z
DTEND:20081217T150000Z
UID:TALK15736@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The spectral statistics of the discrete Laplacian on random d-
 regular graphs (in the limit of large graphs)\, will be discussed. It will
  be shown that in this limit some spectral statistics follow the predictio
 ns of Random Matrix Theory. Counting statistics of cycles on the graphs pl
 ay an important role in the analysis. The level sets of eigenvectors will 
 be shown to display a percollation transition which can be proved by assum
 ing that eigenvectors distribute normally\, with a covariance which can be
  computed using the special properties of the random ensemble of large d-r
 egular graphs.
LOCATION:Seminar Room 1\, Newton Institute
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