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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Squarings of rectangles - Addario-Berry\, L (McGil
l University)
DTSTART;TZID=Europe/London:20150424T100000
DTEND;TZID=Europe/London:20150424T110000
UID:TALK59139AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/59139
DESCRIPTION:Co-author: Nicholas Leavitt (McGill University) \n
\nGrowing random trees\, maps\, and squarings. We
use a growth procedure for binary trees due to Luc
zak and Winkler\, a bijection between binary trees
and irreducible quadrangulations of the hexagon d
ue to Fusy\, Poulalhon and Schaeffer\, and the cla
ssical angular mapping between quadrangulations an
d maps\, to define a growth procedure for maps. Th
e growth procedure is local\, in that every map is
obtained from its predecessor by an operation tha
t only modifies vertices lying on a common face wi
th some fixed vertex. The sequence of maps has an
almost sure limit G\; we show that G is the distri
butional local limit of large\, uniformly random 3
-connected graphs. \n\nA classical result of Brook
s\, Smith\, Stone and Tutte associates squarings o
f rectangles to edge-rooted planar graphs. Our map
growth procedure induces a growing sequence of sq
uarings\, which we show has an almost sure limit:
an infinite squaring of a finite rectangle\, which
almost surely has a unique point of accumulation.
We know almost nothing about the limit\, but it s
hould be in some way related to Liouville quantum
gravity. \n\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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