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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the graph limit approach to random regular grap
hs - Balazs Szegedy (University of Toronto)
DTSTART;TZID=Europe/London:20160713T090000
DTEND;TZID=Europe/London:20160713T094500
UID:TALK66729AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/66729
DESCRIPTION:Let G=G(n\,d) denote the random d-regular \;gr
aph \;on n vertices. A celebrated result by J.
Friedman solves Alon'\;s second eigenvalue con
jecture saying that if d is fixed and n is large t
hen G is close to be Ramanujan. Despite of signifi
cant effort\, much less was known about the struct
ure of the eigenvectors of G. We use a combination
of \;graph \;limit theory and information
theory to prove that every eigenvector of G (when
normalized to have length equal to square root of
n) has an entry distribution that is close to som
e Gaussian distribution in the weak topology. Our
results also work in the more general setting of a
lmost-eigenvectors. We hope our methods will lead
to a general graph limit approach to a large class
of problems on random regular graphs. \;Joint
work with A. Backhausz.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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