Si segnala il seguente seminario:
Lunedì 4 Marzo 2024, ore 16:00, Sala di Consiglio, Dipartimento di
Matematica "Guido Castelnuovo", Sapienza Università di Roma.
*Speaker: *Ilya Losev (University of Cambridge, UK)
*Title: *How long are the arms in Dielectric-Breakdown Model?
*Abstract: *In this talk we will discuss the recent progress on such random
growth models as Diffusion Limited Aggregation (DLA) and
Dielectric-Breakdown Model (DBM) in 2 and 3 dimensions. These models are
believed to exhibit non-equilibrium growth, producing irregular fractal
patterns. The main questions about these processes include finding their
scaling limits and fractal dimensions. However, almost nothing is known
rigorously.
The main result about these models is due to Kesten, who gave a non-trivial
lower bound on the fractal dimension of DLA clusters. The main tool in his
proof was the famous Beurling’s estimate.
We generalize this result to DBM and give a new proof of Kesten’s Theorem.
Our proof does not rely on Beurling’s estimate. Instead, we exploit the
connection between DBM growth properties and multifractal spectrum of the
harmonic measure.
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Vittoria Silvestri
Assistant Professor
Department of Mathematics
University "La Sapienza"
Piazzale Aldo Moro, 5
00185 - Rome
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