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SUMMARY:Graphons and Graphexes as Limits of Sparse Graphs: Part II - Chris
 tian Borgs (Microsoft Research New England)
DTSTART:20180405T143000Z
DTEND:20180405T153000Z
UID:TALK103333@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Graphons and graphexes are limits of graphs which allow us\nto
  model and estimate properties of large-scale networks. In this pair of ta
 lks\, we review the theory of dense graph limits\, and give two alternativ
 e theories for limits of sparse graphs: one leading to unbounded graphons 
 over probability spaces\, and the other leading to bounded graphons (and g
 raphexes) over sigma-finite measure spaces.\n\nTalk II\, to be given by Ch
 ristian Borgs\, will recast limits of dense graphs in terms of exchangeabi
 lity and the Aldous Hoover Theorem\, and generalize this to obtain sparse 
 graphons and graphexes as limits of subgraph samples from sparse graph seq
 uences. This will provide a dual view of sparse graph limits as processes 
 and random measures\, an approach which allows a generalization of many of
  the well-known results and techniques for dense graph sequences.\n
LOCATION:MR12
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