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SUMMARY:How long are the arms in Dielectric-Breakdown Model? - Ilya Losev 
 (Cambridge)
DTSTART:20231031T140000Z
DTEND:20231031T150000Z
UID:TALK207403@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:In this talk we will discuss the recent progress on such rando
 m growth models as Diffusion Limited Aggregation (DLA) and Dielectric-Brea
 kdown Model (DBM) in 2 and 3 dimensions. These models are believed to exhi
 bit non-equilibrium growth\, producing irregular fractal patterns. The mai
 n questions about these processes include finding their scaling limits and
  fractal dimensions. However\, almost nothing is known rigorously.\n\nThe 
 main result about these models is due to Kesten\, who gave a non-trivial l
 ower bound on the fractal dimension of DLA clusters. The main tool in his 
 proof was the famous Beurling’s estimate.  \n\nWe generalize this result
  to DBM and give a new proof of Kesten’s Theorem. Our proof does not rel
 y on Beurling’s estimate. Instead\, we exploit the connection between DB
 M growth properties and multifractal spectrum of the harmonic measure.\nTh
 is talk is based on joint work with Stanislav Smirnov.
LOCATION:MR12
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