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SUMMARY:Convergence of graphs: graphons and growth models - Frederik Søre
nsen (University of Oxford)
DTSTART;VALUE=DATE-TIME:20190307T120000Z
DTEND;VALUE=DATE-TIME:20190307T130000Z
UID:https://talks.ox.ac.uk/talks/id/e971bc7b-37c9-42d0-b7fd-f4c2db010dc5/
DESCRIPTION:In this talk we will discuss two different approaches to provi
ng that a sequence of (random) graphs converges to some limit object.\nFir
stly\, we will introduce a class of functions known as graphons\, which ca
n be thought of as uncountable graphs. We will discuss how to define a sen
sible probabilitistic notion of graph convergence\, and how to utilize the
link between graphs and graphons to translate this notion to the somewhat
"nicer" space of graphons in order to prove that a sequence of graphs con
verges. Secondly\, we will point towards limitations in the above approach
and discuss how the Gromov-Hausdorff-Prokhorov metric can be a useful alt
ernative\, limiting the discussion to sequences of trees. If time permits
we will end the talk by introducing some concrete examples of convergent s
equences of random graphs. The talk is meant to be introductory and will n
ot rely on any previous knowledge of graphs or graph convergence.\nSpeaker
s:\nFrederik Sørensen (University of Oxford)
LOCATION:24-29 St Giles' (Small Lecture Theatre\, Department of Statistics
)\, 24-29 St Giles' OX1 3LB
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e971bc7b-37c9-42d0-b7fd-f4c2db010dc5/
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DESCRIPTION:Talk:Convergence of graphs: graphons and growth models - Frede
rik Sørensen (University of Oxford)
TRIGGER:-PT1H
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