Logarithmic Fluctuations for Internal DLA
Name
Jerison_Logarithmic Fluctuations (arxiv).pdf
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617.63 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Jerison, David S.
Levine, Lionel
Sheffield, Scott Roger
Date Issued
August 2011
Journal
Journal of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Citation
Jerison, David, Lionel Levine, and Scott Sheffield. “Logarithmic Fluctuations for Internal DLA.” Journal of the American Mathematical Society 25.1 (2011).
Version
Author's final manuscript
Abstract
Let each of [superscript n] particles starting at the origin in Z[superscript 2] perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set A(n) of [superscript n] occupied sites is (with high probability) close to a disk B [subscript r] of radius r=√n/pi. We show that the discrepancy between A(n) and the disk is at most logarithmic in the radius: i.e., there is an absolute constant [superscript C] such that with probability [superscript 1], B [subscript r - C log r] C A(pi r[superscript 2]) C B [subscript r+ C log r] for all sufficiently large r.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1090/s0894-0347-2011-00716-9
