Duke Mathematical Journal

Internal DLA and the Gaussian free field

David Jerison, Lionel Levine, and Scott Sheffield

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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.

Article information

Duke Math. J., Volume 163, Number 2 (2014), 267-308.

First available in Project Euclid: 29 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C24: Interface problems; diffusion-limited aggregation


Jerison, David; Levine, Lionel; Sheffield, Scott. Internal DLA and the Gaussian free field. Duke Math. J. 163 (2014), no. 2, 267--308. doi:10.1215/00127094-2430259. https://projecteuclid.org/euclid.dmj/1391007588

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