Subdiffusive fluctuations for internal diffusion limited aggregation
type: Item
instance of: scholarly article
title: Subdiffusive fluctuations for internal diffusion limited aggregation
zbMATH Open document ID: 0835.60086
author: Gregory F. Lawler
published in: The Annals of Probability
publication date: 1996-03-26T00:00:00Z
review text: Internal diffusion limited aggregation is a cluster model in \(\mathbb{Z}^d\) which is formed by independent random walkers starting at the origin, which add the first point they visit, which is not yet contained in the cluster, to it. It was shown by the author with \textit{M. Bramson} and \textit{D. Griffeath} [Ann. Probab. 20, No. 4, 2117-2140 (1992; Zbl 0762.60096)] that the clusters have the limiting shape of a sphere. In the present paper it is shown that for \(d \geq 2\) the fluctuations are of order at most \(n^{1/3}\) up to logarithmic corrections, hence subdiffusive which had been suggested nonrigorously.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B24
zbMATH DE Number: 796533
zbMATH Keywords: cluster growth
zbMATH Keywords: subdiffusive fluctuations
zbMATH Keywords: interfaces
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988377
OpenAlex ID: W2082727051
DOI: 10.1214/AOP/1176988377
description: scientific article; zbMATH DE number 796533