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arXiv · 1101.0596

Internal DLA and the Gaussian free field

David Jerison·Lionel Levine·Scott Sheffield
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Abstract

In previous works, we showed that the internal DLA cluster on \Z^d with t particles is a.s. spherical up to a maximal error of O(\log t) if d=2 and O(\sqrt{\log t}) if d > 2. 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 r^{1-d/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.

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David Jerison, Lionel Levine, Scott Sheffield. 2011-01-03. Internal DLA and the Gaussian free field. https://doi.org/10.1215/00127094-2430259

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