Translator Disclaimer
February 2020 Internal diffusion-limited aggregation with uniform starting points
Itai Benjamini, Hugo Duminil-Copin, Gady Kozma, Cyrille Lucas
Ann. Inst. H. Poincaré Probab. Statist. 56(1): 391-404 (February 2020). DOI: 10.1214/19-AIHP965

Abstract

We study internal diffusion-limited aggregation with uniform starting points on $\mathbb{Z}^{d}$. 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.

Nous étudions le modèle d’agrégation limitée par diffusion interne avec points de départ uniformes sur $\mathbb{Z}^{d}$. Dans ce modèle, chaque nouvelle particule est ajoutée à un point choisi uniformément au hasard parmi ceux de l’agrégat existant. Nous prouvons que l’agrégat normalisé admet comme forme limite la boule euclidienne.

Citation

Download Citation

Itai Benjamini. Hugo Duminil-Copin. Gady Kozma. Cyrille Lucas. "Internal diffusion-limited aggregation with uniform starting points." Ann. Inst. H. Poincaré Probab. Statist. 56 (1) 391 - 404, February 2020. https://doi.org/10.1214/19-AIHP965

Information

Received: 13 April 2018; Revised: 9 November 2018; Accepted: 4 February 2019; Published: February 2020
First available in Project Euclid: 3 February 2020

zbMATH: 07199309
MathSciNet: MR4058992
Digital Object Identifier: 10.1214/19-AIHP965

Subjects:
Primary: 82C24
Secondary: 60J45

Rights: Copyright © 2020 Institut Henri Poincaré

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.56 • No. 1 • February 2020
Back to Top