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SUMMARY:Squarings of rectangles - Addario-Berry\, L (McGill University)
DTSTART:20150424T090000Z
DTEND:20150424T100000Z
UID:TALK59139@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Co-author: Nicholas Leavitt (McGill University) \n\nGrowing ra
 ndom trees\, maps\, and squarings. We use a growth procedure for binary tr
 ees due to Luczak and Winkler\, a bijection between binary trees and irred
 ucible quadrangulations of the hexagon due to Fusy\, Poulalhon and Schaeff
 er\, and the classical angular mapping between quadrangulations and maps\,
  to define a growth procedure for maps. The growth procedure is local\, in
  that every map is obtained from its predecessor by an operation that only
  modifies vertices lying on a common face with some fixed vertex. The sequ
 ence of maps has an almost sure limit G\; we show that G is the distributi
 onal local limit of large\, uniformly random 3-connected graphs. \n\nA cla
 ssical result of Brooks\, Smith\, Stone and Tutte associates squarings of 
 rectangles to edge-rooted planar graphs. Our map growth procedure induces 
 a growing sequence of squarings\, which we show has an almost sure limit: 
 an infinite squaring of a finite rectangle\, which almost surely has a uni
 que point of accumulation. We know almost nothing about the limit\, but it
  should be in some way related to Liouville quantum gravity. \n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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