Internal diffusion-limited aggregation with uniform starting points

Itai Benjamini; Hugo Duminil-Copin; Gady Kozma; Cyrille Lucas

doi:10.1214/19-AIHP965

Internal diffusion-limited aggregation with uniform starting points

Itai Benjamini, Hugo Duminil-Copin, Gady Kozma, Cyrille Lucas

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We study internal diffusion-limited aggregation with uniform starting points on Z(d). In this model, each new particle starts from a vertex chosen uniformly at random on the existing aggregate. We prove that the limiting shape of the aggregate is a Euclidean ball.

Original language	English
Pages (from-to)	391-404
Number of pages	14
Journal	Annales De L Institut Henri Poincare-Probabilites Et Statistiques
Volume	56
Issue number	1
DOIs	https://doi.org/10.1214/19-AIHP965
State	Published - Feb 2020

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/19-AIHP965

http://arxiv.org/abs/1707.03241License: Other

Cite this

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title = "Internal diffusion-limited aggregation with uniform starting points",

abstract = "We study internal diffusion-limited aggregation with uniform starting points on Z(d). In this model, each new particle starts from a vertex chosen uniformly at random on the existing aggregate. We prove that the limiting shape of the aggregate is a Euclidean ball.",

author = "Itai Benjamini and Hugo Duminil-Copin and Gady Kozma and Cyrille Lucas",

note = "The authors would like to thank Vincent Beffara and Vladas Sidoravicius for many fruitful discussions, and Nicolas Curien for referring us to [10]. This paper was partly written during the visit of the second and fourth authors to the Weizmann Institute in Israel. The first author is the incumbent of the Renee and Jay Weiss Professorial Chair. The second author was supported by the EU Marie-Curie RTN CODY, the ERC AG CONFRA, as well as by the Swiss FNS. The third author was supported by the Israel Science Foundation.",

year = "2020",

month = feb,

doi = "10.1214/19-AIHP965",

language = "الإنجليزيّة",

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journal = "Annales De L Institut Henri Poincare-Probabilites Et Statistiques",

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AU - Duminil-Copin, Hugo

AU - Kozma, Gady

AU - Lucas, Cyrille

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N2 - We study internal diffusion-limited aggregation with uniform starting points on Z(d). In this model, each new particle starts from a vertex chosen uniformly at random on the existing aggregate. We prove that the limiting shape of the aggregate is a Euclidean ball.

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M3 - مقالة

SN - 0246-0203

VL - 56

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JO - Annales De L Institut Henri Poincare-Probabilites Et Statistiques

JF - Annales De L Institut Henri Poincare-Probabilites Et Statistiques

IS - 1

ER -

Internal diffusion-limited aggregation with uniform starting points

Abstract

All Science Journal Classification (ASJC) codes

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