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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Graph limits and entropy - Svante Janson (Uppsala
Universitet)
DTSTART;TZID=Europe/London:20160713T110000
DTEND;TZID=Europe/London:20160713T114500
UID:TALK66731AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/66731
DESCRIPTION:The entropy of a graph limit\, or a graphon\, was
essentially defined by Aldous (although in a diffe
rent\, equivalent formulation)\, who showed that i
f a graph limit W has entropy H\, then the entropy
of the distribution of the corresponding random g
raph G(n\,W) is asymptotically n^2 H/2.

Con
sider a hereditary class of graphs Q. Then the num
ber of graphs of order n in Q is asymptotically gi
ven by exp( n^2 H/2)\, where H is the maximum entr
opy of a graph limit that is a limit of graphs in
Q. Moreover\, if this entropy maximizing limit is
unique\, then a uniformly random graph of order n
in Q converges in probability\, as n tends to infi
nity\, to this maximizing graph limit.

As a
n example\, we discuss the entropy maximising grap
h limits for the class of string graphs.

Th
is is based on joint works with Hamed Hatami and B
alasz Szegedy\, and with Andrew Uzzel.

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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