Internal DLA and the Gaussian free field
Name
Jerison_Internal dla.pdf
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620.68 KB
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Adobe PDF
Checksum (MD5)
24258b6ef90334e35a774c59d5c489b9
Author(s)
Jerison, David S.
Levine, Lionel
Sheffield, Scott Roger
Date Issued
February 2014
Journal
Duke Mathematical Journal
Publisher
Duke University Press
Citation
Jerison, David, Lionel Levine, and Scott Sheffield. “Internal DLA and the Gaussian Free Field.” Duke Mathematical Journal 163, no. 2 (February 2014): 267–308.
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1215/00127094-2430259
