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SUMMARY:On the graph limit approach to random regular graphs - Balazs Szeg
 edy (University of Toronto)
DTSTART:20160713T080000Z
DTEND:20160713T084500Z
UID:TALK66729@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Let G=G(n\,d) denote the random d-regular&nbsp\;graph&nbsp\;on
  n vertices. A celebrated result by J. Friedman solves Alon&#39\;s second 
 eigenvalue conjecture saying that if d is fixed and n is large then G is c
 lose to be Ramanujan. Despite of significant effort\, much less was known 
 about the structure of the eigenvectors of G. We use a combination of&nbsp
 \;graph&nbsp\;limit theory and information theory to prove that every eige
 nvector of G (when normalized to have length equal to square root of n) ha
 s an entry distribution that is close to some Gaussian distribution in the
  weak topology. Our results also work in the more general setting of almos
 t-eigenvectors. We hope our methods will lead to a general graph limit app
 roach to a large class of problems on random regular graphs.&nbsp\;Joint w
 ork with A. Backhausz.
LOCATION:Seminar Room 1\, Newton Institute
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