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CATEGORIES:Combinatorics Seminar
SUMMARY:Graphons and Graphexes as Limits of Sparse Graphs:
Part II - Christian Borgs (Microsoft Research New
England)
DTSTART;TZID=Europe/London:20180405T153000
DTEND;TZID=Europe/London:20180405T163000
UID:TALK103333AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/103333
DESCRIPTION:Graphons and graphexes are limits of graphs which
allow us\nto model and estimate properties of larg
e-scale networks. In this pair of talks\, we revie
w the theory of dense graph limits\, and give two
alternative theories for limits of sparse graphs:
one leading to unbounded graphons over probability
spaces\, and the other leading to bounded graphon
s (and graphexes) over sigma-finite measure spaces
.\n\nTalk II\, to be given by Christian Borgs\, wi
ll recast limits of dense graphs in terms of excha
ngeability and the Aldous Hoover Theorem\, and gen
eralize this to obtain sparse graphons and graphex
es as limits of subgraph samples from sparse graph
sequences. This will provide a dual view of spars
e 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
CONTACT:Andrew Thomason
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