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CATEGORIES:Probability
SUMMARY:On the continuity of SLE(k) curves in k and their
behavior at the tip - Fredrik Johansson Viklund (C
olumbia)
DTSTART;TZID=Europe/London:20120529T163000
DTEND;TZID=Europe/London:20120529T173000
UID:TALK38037AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/38037
DESCRIPTION:On the continuity of SLE(k) curves in k and their
behavior at the tip\n\nThe Schramm-Loewner evoluti
on with parameter k > 0\, SLE(k)\, is a\nfamily of
random fractal curves constructed using the Loewn
er\ndifferential equation driven by a standard Bro
wnian motion times the\nsquare-root of k. These cu
rves arise as scaling limits of cluster\ninterface
s in certain planar critical lattice models. A nat
ural\nquestion that has been asked is whether the
(parameterized) SLE(k)\ncurves almost surely chang
e continuously if the Brownian motion sample\nis k
ept fixed while k is varied.\n\nIn the talk I will
present recent work giving a positive answer to\n
this question\, at least for an interval of k. I w
ill also give some\nbackground on SLE and the Loew
ner equation\, and describe the basic\ntools we us
e for the proof\, in particular certain bounds\nch
aracterizing the behavior of a growing SLE(k) curv
e close to its\ntip.\n\nThe talk is based on joint
work with Steffen Rohde and Carto Wong\, and\nGre
g Lawler.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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