Abstract
Internal DLA (IDLA) is an internal aggregation model in which particles perform random walks from the origin, in turn, and stop upon reaching an unoccupied site. Levine and Peres showed that, when particles start instead from fixed multiple-point distributions, the modified IDLA processes have deterministic scaling limits related to a certain obstacle problem. In this paper, we investigate the convergence rate of this “extended source” IDLA in the plane to its scaling limit. We show that, if \(\delta \) is the lattice size, fluctuations of the IDLA occupied set are at most of order \(\delta ^{3/5}\) from its scaling limit, with probability at least \(1-e^{-1/\delta ^{2/5}}\).
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Acknowledgements
I would like to thank Professor David Jerison and the MIT UROP+ program (organized by Slava Gerovitch) for making this project possible. I would like to especially thank David Jerison and Pu Yu (MIT Department of Mathematics) for their mentorship throughout. This research was partially supported by a grant from the National Science Foundation (NSF).
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Open Access funding provided by the MIT Libraries. This research was partially supported by a grant from the National Science Foundation (NSF).
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This research was partially supported by a grant from the National Science Foundation (NSF).
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Darrow, D. A Convergence Rate for Extended-Source Internal DLA in the Plane. Potential Anal 61, 35–64 (2024). https://doi.org/10.1007/s11118-023-10102-8
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DOI: https://doi.org/10.1007/s11118-023-10102-8