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SUMMARY:Graph limits and entropy - Svante Janson (Uppsala Universitet)
DTSTART:20160713T100000Z
DTEND:20160713T104500Z
UID:TALK66731@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The entropy of a graph limit\, or a graphon\, was essentially 
 defined by Aldous (although in a different\, equivalent formulation)\, who
  showed that if a graph limit W has entropy H\, then the entropy of the di
 stribution of the corresponding random graph G(n\,W) is asymptotically n^2
  H/2.<br><br>Consider a hereditary class of graphs Q. Then the number of g
 raphs of order n in Q is asymptotically given by exp( n^2 H/2)\, where H i
 s the maximum entropy of a graph limit that is a limit of graphs in Q. Mor
 eover\, if this entropy maximizing limit is unique\, then a uniformly rand
 om graph of order n in Q converges in probability\, as n tends to infinity
 \, to this maximizing graph limit.<br><br>As an example\, we discuss the e
 ntropy maximising graph limits for the class of string graphs.<br><br>This
  is based on joint works with Hamed Hatami and Balasz Szegedy\, and with A
 ndrew Uzzel.<br>
LOCATION:Seminar Room 1\, Newton Institute
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