Internal DLA and the Gaussian free field
Author(s)Jerison, David S.; Levine, Lionel; Sheffield, Scott Roger
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In previous works, we showed that the internal diffusion-limited aggregation (DLA) cluster on Z[superscript d] with t particles is almost surely spherical up to a maximal error of O(logt) if d=2 and O(logt√) if d≥3. 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[superscript 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Duke Mathematical Journal
Duke University Press
Jerison, David, Lionel Levine, and Scott Sheffield. “Internal DLA and the Gaussian Free Field.” Duke Mathematical Journal 163, no. 2 (February 2014): 267–308.