Random stable looptrees
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | Random stable looptrees |
| 2. | Creator | Author's name, affiliation, country | Nicolas Curien; CNRS & University Paris 6; France |
| 2. | Creator | Author's name, affiliation, country | Igor Kortchemski; DMA, Ecole Normale Supérieure |
| 3. | Subject | Discipline(s) | |
| 3. | Subject | Keyword(s) | Stable processes; Random metric spaces; Random non-crossing configurations |
| 3. | Subject | Subject classification | Primary 60F17, 60G52 ; secondary 05C80 |
| 4. | Description | Abstract | We introduce a class of random compact metric spaces $\mathscr{L}_{\alpha}$ indexed by $\alpha~\in(1,2)$ and which we call stable looptrees. They are made of a collection of random loops glued together along a tree structure, and can be informally be viewed as dual graphs of $\alpha$-stable Lévy trees. We study their properties and prove in particular that the Hausdorff dimension of $ \mathscr{L}_{\alpha}$ is almost surely equal to $\alpha$. We also show that stable looptrees are universal scaling limits, for the Gromov-Hausdorff topology, of various combinatorial models. In a companion paper, we prove that the stable looptree of parameter $ \frac{3}{2}$ is the scaling limit of cluster boundaries in critical site-percolation on large random triangulations. |
| 5. | Publisher | Organizing agency, location | |
| 6. | Contributor | Sponsor(s) | French “Agence Nationale de la Recherche” ANR-08-BLAN-0190 |
| 7. | Date | (YYYY-MM-DD) | 2014-11-11 |
| 8. | Type | Status & genre | Peer-reviewed Article |
| 8. | Type | Type | |
| 9. | Format | File format | PDF, Untitled () |
| 10. | Identifier | Uniform Resource Identifier | http://ejp.ejpecp.org/article/view/2732 |
| 10. | Identifier | Digital Object Identifier | 10.1214/EJP.v19-2732 |
| 11. | Source | Journal/conference title; vol., no. (year) | Electronic Journal of Probability; Vol 19 |
| 12. | Language | English=en | en |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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