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SUMMARY:Small-particle limits in a regularized Laplacian random growth mod
 el - Turner\, A (Lancaster University)
DTSTART:20150317T140000Z
DTEND:20150317T150000Z
UID:TALK58428@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Fredrik Johansson Viklund (Uppsala University)\, A
 lan Sola (University of Cambridge) \n\nIn 1998 Hastings and Levitov propos
 ed a one-parameter family of models for planar random growth in which clus
 ters are represented as compositions of conformal mappings. This family in
 cludes physically occurring processes such as diffusion-limited aggregatio
 n (DLA)\, dielectric breakdown and the Eden model for biological cell grow
 th. In the simplest case of the model (corresponding to the parameter alph
 a=0)\, James Norris and I showed how the Brownian web arises in the limit 
 resulting from small particle size and rapid aggregation. In particular th
 is implies that beyond a certain time\, all newly aggregating particles sh
 are a single common ancestor. I shall show how small changes in alpha resu
 lt in the emergence of branching structures within the model so that\, bey
 ond a certain time\, the number of common ancestors is a random number who
 se distribution can be obtained. This is based on joint work with Fredrik 
 Johansson Viklund (Uppsala) and Alan Sola (Cambridge).\n
LOCATION:Seminar Room 1\, Newton Institute
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