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CATEGORIES:Probability
SUMMARY:Fluctuation results for Hastings-Levitov planar gr
owth - Vittoria Silvestri (Cambridge)
DTSTART;TZID=Europe/London:20150526T163000
DTEND;TZID=Europe/London:20150526T173000
UID:TALK59485AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/59485
DESCRIPTION:In 1998 the physicists Hastings and Levitov introd
uced a family of continuum models to describe a ra
nge of physical phenomena of planar aggregation/di
ffusion. These consist of growing random clusters
on the complex plane\, which are built by iterated
composition of random conformal maps.It was shown
by Norris and Turner (2012) that in the case of i
.d.d. maps the limiting shape of these clusters is
a disc: in this talk I will show that the fluctua
tions around this shape are given by a random holo
morphic Gaussian field F on {|z| > 1}\, of which I
will provide an explicit construction. When the c
luster is allowed to grow indefinitely\, I will sh
ow that the boundary values of F converge to a dis
tribution-valued Fractional Gaussian field on the
unit circle\, which is log-correlated\, and critic
al in a sense that I will explain.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:John Shimmon
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