The number of unbounded components in the Poisson Boolean model of continuum percolation in hyperbolic space
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1. | Title | Title of document | The number of unbounded components in the Poisson Boolean model of continuum percolation in hyperbolic space |
2. | Creator | Author's name, affiliation, country | Johan Harald Tykesson; Chalmers University of Technology |
3. | Subject | Discipline(s) | |
3. | Subject | Keyword(s) | continuum percolation; phase transitions; hyperbolic space |
3. | Subject | Subject classification | 82B21; 82B43 |
4. | Description | Abstract | We consider the Poisson Boolean model of continuum percolation with balls of fixed radius $R$ in $n$-dimensional hyperbolic space $H^n$. Let $\lambda$ be the intensity of the underlying Poisson process, and let $N_C$ denote the number of unbounded components in the covered region. For the model in any dimension we show that there are intensities such that $N_C=\infty$ a.s. if $R$ is big enough. In $H^2$ we show a stronger result: for any $R$ there are two intensities $\lambda_c$ and $\lambda_u$ where $0< \lambda_c < \lambda _u < \infty$, such that$N_C=0$ for $\lambda \in [0,\lambda_c]$, $N_C=\infty$ for $\lambda \in (\lambda_c,\lambda_u)$ and $N_C=1$ for $\lambda \in [\lambda_u, \infty)$. |
5. | Publisher | Organizing agency, location | |
6. | Contributor | Sponsor(s) | Swedish Natural Science Research Council |
7. | Date | (YYYY-MM-DD) | 2007-11-04 |
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/460 |
10. | Identifier | Digital Object Identifier | 10.1214/EJP.v12-460 |
11. | Source | Journal/conference title; vol., no. (year) | Electronic Journal of Probability; Vol 12 |
12. | Language | English=en | |
14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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