Greedy polyominoes and first-passage times on random Voronoi tilings
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | Greedy polyominoes and first-passage times on random Voronoi tilings |
| 2. | Creator | Author's name, affiliation, country | Raphaël Rossignol; Université Joseph Fourier Grenoble 1; France |
| 2. | Creator | Author's name, affiliation, country | Leandro P. R. Pimentel; Federal University of Rio de Janeiro, Brazil; Brazil |
| 3. | Subject | Discipline(s) | |
| 3. | Subject | Keyword(s) | Random Voronoi tiling; Delaunay graph; First passage percolation; connective constant; greedy animal; random walk |
| 3. | Subject | Subject classification | 60K35; 60D05 |
| 4. | Description | Abstract | Let $\mathcal{N}$ be distributed as a Poisson random set on $\mathbb{R}^d$, $d\geq 2$, with intensity comparable to the Lebesgue measure. Consider the Voronoi tiling of $\mathbb{R}^d$, $\{C_v\}_{v\in \mathcal{N}}$, where $C_v$ is composed of points $\mathbf{x}\in\mathbb{R}^d$ that are closer to $v\in\mathcal{N}$ than to any other $v'\in\mathcal{N}$. A polyomino $\mathcal{P}$ of size $n$ is a connected union (in the usual $\mathbb{R}^d$ topological sense) of $n$ tiles, and we denote by $\Pi_n$ the collection of all polyominos $\mathcal{P}$ of size $n$ containing the origin. Assume that the weight of a Voronoi tile $C_v$ is given by $F(C_v)$, where $F$ is a nonnegative functional on Voronoi tiles. In this paper we investigate for some functionals $F$, mainly when $F(C_v)$ is a polynomial function of the number of faces of $C_v$, the tail behavior of the maximal weight among polyominoes in $\Pi_n$: $F_n=F_n(\mathcal{N}):=\max_{\mathcal{P}\in\Pi_n} \sum_{v\in \mathcal{P}} F(C_v)$. Next we apply our results to study self-avoiding paths, first-passage percolation models and the stabbing number on the dual graph, named the Delaunay triangulation. As the main application we show that first passage percolation has at most linear variance. |
| 5. | Publisher | Organizing agency, location | |
| 6. | Contributor | Sponsor(s) | Swiss National Science Foundation, Fundação de Amparo a Pesquisa do Estado de São Paulo and The Netherlands Organisation for Scientific Research. |
| 7. | Date | (YYYY-MM-DD) | 2012-02-01 |
| 8. | Type | Status & genre | Peer-reviewed Article |
| 8. | Type | Type | |
| 9. | Format | File format | |
| 10. | Identifier | Uniform Resource Identifier | http://ejp.ejpecp.org/article/view/1788 |
| 10. | Identifier | Digital Object Identifier | 10.1214/EJP.v17-1788 |
| 11. | Source | Journal/conference title; vol., no. (year) | Electronic Journal of Probability; Vol 17 |
| 12. | Language | English=en | en |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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