Clustering and percolation of point processes
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | Clustering and percolation of point processes |
| 2. | Creator | Author's name, affiliation, country | Bartlomiej Blaszczyszyn; INRIA / ENS Paris; France |
| 2. | Creator | Author's name, affiliation, country | Dhandapani Yogeshwaran; Technion - Israel Institute of Technology; Israel |
| 3. | Subject | Discipline(s) | |
| 3. | Subject | Keyword(s) | point process, Boolean model, percolation, phase transition, shot-noise fields, level-sets, directionally convex ordering, perturbed lattices, determinantal, sub-Poisson point processes. |
| 3. | Subject | Subject classification | Primary 60G55, 82B43, 60E15 ; Secondary 60K35, 60D05, 60G60 |
| 4. | Description | Abstract | We are interested in phase transitions in certain percolation models on point processes and their dependence on clustering properties of the point processes. We show that point processes with smaller void probabilities and factorial moment measures than the stationary Poisson point process exhibit non-trivial phase transition in the percolation of some coverage models based on level-sets of additive functionals of the point process. Examples of such point processes are determinantal point processes, some perturbed lattices and more generally, negatively associated point processes. Examples of such coverage models are k-coverage in the Boolean model (coverage by at least k grains), and SINR-coverage (coverage if the signal to-interference-and-noise ratio is large). In particular, we answer in affirmative the hypothesis of existence of phase transition in the percolation of k-faces in the Cech simplicial complex (called also clique percolation) on point processes which cluster less than the Poisson process. We also construct a Cox point process, which is "more clustered” than the Poisson point process and whose Boolean model percolates for arbitrarily small radius. This shows that clustering (at least, as detected by our specific tools) does not always “worsen” percolation, as well as that upper-bounding this cluster-ing by a Poisson process is a consequential assumption for the phase transition to hold. |
| 5. | Publisher | Organizing agency, location | |
| 6. | Contributor | Sponsor(s) | ENS, Paris ; INRIA, Paris ; EADS, Paris ; Israel Science Foundation (No: 853/10) ; AFOSR (No: FA8655-11-1-3039). |
| 7. | Date | (YYYY-MM-DD) | 2013-07-31 |
| 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/2468 |
| 10. | Identifier | Digital Object Identifier | 10.1214/EJP.v18-2468 |
| 11. | Source | Journal/conference title; vol., no. (year) | Electronic Journal of Probability; Vol 18 |
| 12. | Language | English=en | en |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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