Scaling limits of fluctuations of extended-source internal DLA
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11854_2023_Article_280.pdf
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633.39 KB
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Author(s)
Darrow, David
Date Issued
June 20, 2023
Publisher
The Hebrew University Magnes Press
Citation
Darrow, David. 2023. "Scaling limits of fluctuations of extended-source internal DLA."
Version
Final published version
Abstract
Abstract
In a previous work, we showed that the 2D, extended-source internal DLA (IDLA) of Levine and Peres is δ3/5-close to its scaling limit, if δ is the lattice size. In this paper, we investigate the scaling limits of the fluctuations themselves. Namely, we show that two naturally defined error functions, which measure the “lateness” of lattice points at one time and at all times, respectively, converge to geometry-dependent Gaussian random fields. We use these results to calculate point-correlation functions associated with the fluctuations of the flow. Along the way, we demonstrate similar δ3/5 bounds on the fluctuations of the related divisible sandpile model of Levine and Peres, and we generalize the results of our previous work to a larger class of extended sources.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s11854-023-0280-5
