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SUMMARY:Scaling limit of the largest clusters in critical percolation and 
 FK-Ising models in two dimensions - Dr Demeter Kiss\, Statistical Laborato
 ry\, Cambridge
DTSTART:20141028T163000Z
DTEND:20141028T173000Z
UID:TALK55838@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:Consider the percolation model with parameter p on hexagonal l
 attice with mesh-size \\eta: We paint each hexagon by red with probability
  p\, and blue with probability 1-p\, independently from each\nother. At p 
 = 1/2\, macroscopic red and blue clusters (connected components) coexist. 
 We show that at p = 1/2\, as \\eta tends to 0\, the macroscopic red cluste
 rs seen as closed subsets of the plane converge to\na collection of contin
 uum clusters. Similar result holds for the normalized counting measure of 
 the hexagons in red clusters.\nWe discuss the background of the results ab
 ove\, and their applications including a construction of scaling limit of 
 frozen percolation and\nalternative constructions for near-critical percol
 ation and for the magnetization field in the critical Ising model.\nOur re
 sults are based on papers by Garban\, Pete and Schramm\, and it is joint w
 ork With Federico Camia and Rene Conijn.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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