Random stable looptrees

Understand

We introduce a class of random compact metric spaces 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 L\'evy trees.
• We study their properties and prove in particular that the Hausdorff dimension of 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.