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Cylindrical Hastings Levitov
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abstract
We define a Hastings-Levitov$(0)$ process on a cylinder and prove that the process converges to Stationary Hastings Levitov$(0)$ under appropriate particle size scaling that depends on the radius of the cylinder. The Stationary Hastings Levitov$(0)$ was shown by Berger, Procaccia and Turner to admit tight particle sizes, without a priori particle size normalization, thus it serves as a good model for the phenomenon of diffusion limited aggregation. Technical challenge, in this paper, is in taking the spatial limit together with the correct slit map normalization. This result also shows that the early life of the Hastings Levitov$(0)$ process in the small particle limit, spatially scaled so the slits have unit length, behaves like the Stationary Hastings Levitov$(0)$.
Forward citations
Cited by 2 Pith papers
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One-arm domination time in Cylindrical Hastings-Levitov$(0)$
In cylindrical Hastings-Levitov(0) aggregation, the expected one-arm domination time is of order N^2/λ^3, with an exponential tail, and the expected number of trees is asymptotically π N/λ.
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Sharp asymptotics for the tree-completion time in cylindrical Hastings--Levitov$(0)$
The expected time until no new tree is born in cylindrical Hastings-Levitov(0) aggregation is asymptotically log(N)/(2λ), confirming the conjectured sharp constant.
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