The bi-dimensional Directed IDLA forest
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866911212299616256 |
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| author | Chenavier, Nicolas Coupier, David Rousselle, Arnaud |
| author_facet | Chenavier, Nicolas Coupier, David Rousselle, Arnaud |
| contents | We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on $\mathbf{Z}^2$ with infinitely many sources that are the points of the vertical axis $I(\infty)=\{0\}\times\mathbf{Z}$. Various properties are provided, such as stationarity, mixing, stabilization and shape theorems. Our results allow us to define a new directed (w.r.t. the horizontal direction) random forest spanning $\mathbf{Z}^2$, based on an IDLA protocol, which is invariant in distribution w.r.t. vertical translations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_12090 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The bi-dimensional Directed IDLA forest Chenavier, Nicolas Coupier, David Rousselle, Arnaud Probability We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on $\mathbf{Z}^2$ with infinitely many sources that are the points of the vertical axis $I(\infty)=\{0\}\times\mathbf{Z}$. Various properties are provided, such as stationarity, mixing, stabilization and shape theorems. Our results allow us to define a new directed (w.r.t. the horizontal direction) random forest spanning $\mathbf{Z}^2$, based on an IDLA protocol, which is invariant in distribution w.r.t. vertical translations. |
| title | The bi-dimensional Directed IDLA forest |
| topic | Probability |
| url | https://arxiv.org/abs/2009.12090 |