@article{EJP2732,
author = {Nicolas Curien and Igor Kortchemski},
title = {Random stable looptrees},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Stable processes; Random metric spaces; Random non-crossing configurations},
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.},
pages = {no. 108, 1-35},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2732},
url = {http://ejp.ejpecp.org/article/view/2732}}