Shape exclusion for diffusion-limited aggregation
For diffusion-limited aggregation on $\mathbb{Z}^d$ with $d \geq 2$, 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.
Authors
- Amir Dembo
- Matthew Junge (ORCID: https://orcid.org/0000-0003-1940-784X)
Publication Details
- Journal
- arXiv (Cornell University)
- Published
- 2026-10-27
- DOI
- https://doi.org/10.48550/arxiv.2610.37625
- Primary Topic
- Stochastic processes and statistical mechanics
- Type
- preprint