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SUMMARY:Fluctuation results for Hastings-Levitov planar growth - Vittoria 
 Silvestri (Cambridge)
DTSTART:20150526T153000Z
DTEND:20150526T163000Z
UID:TALK59485@talks.cam.ac.uk
CONTACT:John Shimmon
DESCRIPTION:In 1998 the physicists Hastings and Levitov introduced a famil
 y of continuum models to describe a range of physical phenomena of planar 
 aggregation/diffusion. These consist of growing random clusters on the com
 plex plane\, which are built by iterated composition of random conformal m
 aps.It was shown by Norris and Turner (2012) that in the case of i.d.d. ma
 ps the limiting shape of these clusters is a disc: in this talk I will sho
 w that the fluctuations around this shape are given by a random holomorphi
 c Gaussian field F on {|z| > 1}\, of which I will provide an explicit cons
 truction. When the cluster is allowed to grow indefinitely\, I will show t
 hat the boundary values of F converge to a distribution-valued Fractional 
 Gaussian field on the unit circle\, which is log-correlated\, and critical
  in a sense that I will explain.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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