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SUMMARY:Small-particle scaling limits in a regularized Laplacian growth mo
 del - Alan Sola  (Cambridge)
DTSTART:20131029T163000Z
DTEND:20131029T173000Z
UID:TALK47770@talks.cam.ac.uk
CONTACT:24873
DESCRIPTION:We study a regularized version of the Hastings-Levitov\nmodel 
 of Laplacian random growth. In addition to the usual feedback\nparameter a
 lpha>0\, this regularized version features a smoothing\nparameter sigma>0.
  Simulations of the resulting growth processes\nreveal non-trivial feature
 s that differ from those observed in HL(0).\nWe prove convergence of rando
 m clusters\, in the limit as the size of\nthe individual aggregating parti
 cles tends to zero\, to deterministic\nlimits\, provided the smoothing par
 ameter does not tend to zero too\nfast. We also study scaling limits of th
 e harmonic measure flow on the\nboundary\, and show that it can be describ
 ed in terms of stopped\nBrownian webs on the circle. In contrast to the ca
 se alpha=0\, the\nflow does not always collapse into a single Brownian mot
 ion\, which can\nbe interpreted as a random number of infinite branches be
 ing present\nin the clusters. Joint work with Fredrik Johansson Viklund an
 d Amanda Turner. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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