Internal Diffusion Limited Aggregation with Critical Branching Random Walks
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866917016805310464 |
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| author | Asselah, Amine Silvestri, Vittoria Taggi, Lorenzo |
| author_facet | Asselah, Amine Silvestri, Vittoria Taggi, Lorenzo |
| contents | Internal Diffusion Limited Aggregation is an interacting particle system that describes the growth of a random cluster governed by the boundary harmonic measure seen from an internal point. Our paper studies IDLA in $\mathbb{Z}^d$ driven by critical branching random walks. We prove that, unlike classical IDLA, this process exhibits a phase transition in the dimension. More precisely, we establish the existence of a spherical shape theorem in dimension $d\geq 3$ and the absence of a spherical shape theorem for $d \leq 2$. Our bounds on the inner and outer worst deviations are of polynomial nature, which we expect to be a feature of this model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Internal Diffusion Limited Aggregation with Critical Branching Random Walks Asselah, Amine Silvestri, Vittoria Taggi, Lorenzo Probability Internal Diffusion Limited Aggregation is an interacting particle system that describes the growth of a random cluster governed by the boundary harmonic measure seen from an internal point. Our paper studies IDLA in $\mathbb{Z}^d$ driven by critical branching random walks. We prove that, unlike classical IDLA, this process exhibits a phase transition in the dimension. More precisely, we establish the existence of a spherical shape theorem in dimension $d\geq 3$ and the absence of a spherical shape theorem for $d \leq 2$. Our bounds on the inner and outer worst deviations are of polynomial nature, which we expect to be a feature of this model. |
| title | Internal Diffusion Limited Aggregation with Critical Branching Random Walks |
| topic | Probability |
| url | https://arxiv.org/abs/2510.13733 |