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SUMMARY:On the continuity of SLE(k) curves in k and their behavior at the 
 tip - Fredrik Johansson Viklund (Columbia)
DTSTART:20120529T153000Z
DTEND:20120529T163000Z
UID:TALK38037@talks.cam.ac.uk
CONTACT:24873
DESCRIPTION:On the continuity of SLE(k) curves in k and their behavior at 
 the tip\n\nThe Schramm-Loewner evolution with parameter k > 0\, SLE(k)\, i
 s a\nfamily of random fractal curves constructed using the Loewner\ndiffer
 ential equation driven by a standard Brownian motion times the\nsquare-roo
 t of k. These curves arise as scaling limits of cluster\ninterfaces in cer
 tain planar critical lattice models. A natural\nquestion that has been ask
 ed is whether the (parameterized) SLE(k)\ncurves almost surely change cont
 inuously if the Brownian motion sample\nis kept fixed while k is varied.\n
 \nIn the talk I will present recent work giving a positive answer to\nthis
  question\, at least for an interval of k. I will also give some\nbackgrou
 nd on SLE and the Loewner equation\, and describe the basic\ntools we use 
 for the proof\, in particular certain bounds\ncharacterizing the behavior 
 of a growing SLE(k) curve close to its\ntip.\n\nThe talk is based on joint
  work with Steffen Rohde and Carto Wong\, and\nGreg Lawler.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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