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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Growth of Stationary Hastings-Levitov
AU - Berger, Noam
AU - Procaccia, Eviatar B.
AU - Turner, Amanda
N1 - 32 pages, 2 figures
PY - 2022/10/31
Y1 - 2022/10/31
N2 - We construct and study a stationary version of the Hastings-Levitov$(0)$ model. We prove that, unlike in the classical HL$(0)$ model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL$(0)$ is proposed as a potential candidate for a stationary off-lattice variant of Diffusion Limited Aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL$(0)$ converge to the graph of Brownian motion which has fractal dimension $3/2$. Moreover we show that trees with $n$ particles reach a height of order $n^{2/3}$, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.
AB - We construct and study a stationary version of the Hastings-Levitov$(0)$ model. We prove that, unlike in the classical HL$(0)$ model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL$(0)$ is proposed as a potential candidate for a stationary off-lattice variant of Diffusion Limited Aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL$(0)$ converge to the graph of Brownian motion which has fractal dimension $3/2$. Moreover we show that trees with $n$ particles reach a height of order $n^{2/3}$, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.
KW - math.PR
KW - math-ph
KW - math.MP
U2 - 10.1214/21-AAP1761
DO - 10.1214/21-AAP1761
M3 - Journal article
VL - 32
SP - 3331
EP - 3330
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 5
ER -