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Shape exclusion for diffusion-limited aggregation
Abstract
For diffusion-limited aggregation on ℤd with d ≥ 2, we rule out convergence in volume to bounded regions with boundary measure zero. Moreover, the number of boundary edges grows linearly. For Euclidean DLA in dimensions $2$, $3$, $8$, and $24$, we prove an analogous shape exclusion.
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BibTeX
@misc{dembo2026shape,
title = {{Shape exclusion for diffusion-limited aggregation}},
author = {Amir Dembo and Matthew Junge},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37625},
eprint = {2610.37625},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37625},
}
RIS
TY - UNPB
TI - Shape exclusion for diffusion-limited aggregation
AU - Amir Dembo
AU - Matthew Junge
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37625
UR - https://arxiv.org/abs/2610.37625
AB - For diffusion-limited aggregation on ℤ^d with d ≥ 2, we rule out convergence in volume to bounded regions with boundary measure zero. Moreover, the number of boundary edges grows linearly. For Euclidean DLA in dimensions $2$, $3$, $8$, and $24$, we prove an analogous shape exclusion.
ER -