A Convergence Rate for Extended-Source Internal DLA in the Plane
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11118_2023_Article_10102.pdf
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998.04 KB
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Author(s)
Darrow, David
Date Issued
October 16, 2023
Journal
Potential Analysis
Publisher
Springer Netherlands
Citation
Darrow, David. 2023. "A Convergence Rate for Extended-Source Internal DLA in the Plane." Potential Analysis.
Version
Final published version
Abstract
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
$$\delta $$
δ
is the lattice size, fluctuations of the IDLA occupied set are at most of order
$$\delta ^{3/5}$$
δ
3
/
5
from its scaling limit, with probability at least
$$1-e^{-1/\delta ^{2/5}}$$
1
-
e
-
1
/
δ
2
/
5
.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s11118-023-10102-8
