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1 February 2014 Internal DLA and the Gaussian free field
David Jerison, Lionel Levine, Scott Sheffield
Duke Math. J. 163(2): 267-308 (1 February 2014). DOI: 10.1215/00127094-2430259

Abstract

In previous works, we showed that the internal diffusion-limited aggregation (DLA) cluster on Zd with t particles is almost surely spherical up to a maximal error of O(logt) if d=2 and O(logt) if d3. This paper addresses average error: in a certain sense, the average deviation of internal DLA from its mean shape is of constant order when d=2 and of order r1d/2 (for a radius r cluster) in general. Appropriately normalized, the fluctuations (taken over time and space) scale to a variant of the Gaussian free field.

Citation

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David Jerison. Lionel Levine. Scott Sheffield. "Internal DLA and the Gaussian free field." Duke Math. J. 163 (2) 267 - 308, 1 February 2014. https://doi.org/10.1215/00127094-2430259

Information

Published: 1 February 2014
First available in Project Euclid: 29 January 2014

zbMATH: 1296.60113
MathSciNet: MR3161315
Digital Object Identifier: 10.1215/00127094-2430259

Subjects:
Primary: 60G50
Secondary: 60K35, 82C24

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 2 • 1 February 2014
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