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| Autori principali: | , , |
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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2604.21142 |
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| _version_ | 1866915950903689216 |
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| author | Bou-Rabee, Ahmed Silvestri, Vittoria Yadin, Ariel |
| author_facet | Bou-Rabee, Ahmed Silvestri, Vittoria Yadin, Ariel |
| contents | Internal DLA is a discrete random growth model describing growing clusters of particles. Its limiting shape and fluctuations are well understood when the underlying graph is the $d$-dimensional lattice or the cylinder $\mathbb{Z}_N \times \mathbb{Z}$. In the latter geometry, the average fluctuations of IDLA have been shown to converge to the GFF. In this note we generalise this result by showing that, for any vertex-transitive base graph $V_N$ satisfying an eigenvalue convergence condition, the average fluctuations of IDLA on the cylinder $V_N \times \mathbb{Z}$ are given by a GFF. On the way, we present an improved bound on the clusters' maximal fluctuations, which is of independent interest and which implies a shape theorem for IDLA on $V_N \times \mathbb{Z}$ for any vertex-transitive base graph $V_N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21142 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gaussian fluctuations for Internal DLA on cylinders Bou-Rabee, Ahmed Silvestri, Vittoria Yadin, Ariel Probability Internal DLA is a discrete random growth model describing growing clusters of particles. Its limiting shape and fluctuations are well understood when the underlying graph is the $d$-dimensional lattice or the cylinder $\mathbb{Z}_N \times \mathbb{Z}$. In the latter geometry, the average fluctuations of IDLA have been shown to converge to the GFF. In this note we generalise this result by showing that, for any vertex-transitive base graph $V_N$ satisfying an eigenvalue convergence condition, the average fluctuations of IDLA on the cylinder $V_N \times \mathbb{Z}$ are given by a GFF. On the way, we present an improved bound on the clusters' maximal fluctuations, which is of independent interest and which implies a shape theorem for IDLA on $V_N \times \mathbb{Z}$ for any vertex-transitive base graph $V_N$. |
| title | Gaussian fluctuations for Internal DLA on cylinders |
| topic | Probability |
| url | https://arxiv.org/abs/2604.21142 |