20 citations · 57 across the 15 of their papers we have counts for
16 papers
Phase transition for tree-rooted maps
Marie Albenque, Éric Fusy, Zéphyr Salvy
We introduce a model of tree-rooted planar maps weighted by their number of -connected blocks. We study its enumerative properties and prove that it undergoes a phase transition…
Refined Horton-Strahler numbers I: a discrete bijection
Louigi Addario-Berry, Marie Albenque, Serte Donderwinkel +1
The Horton-Strahler number of a rooted tree is the height of the tallest complete binary tree that can be homeomorphically embedded in . The number of full binary trees with…
Random cubic planar graphs converge to the Brownian sphere
Marie Albenque, Éric Fusy, Thomas Lehéricy
In this paper, the scaling limit of random connected cubic planar graphs (respectively multigraphs) is shown to be the Brownian sphere. The proof consists in essentially two main s…
Geometric properties of spin clusters in random triangulations coupled with an Ising Model
Marie Albenque, Laurent Ménard
We investigate the geometry of a typical spin cluster in random triangulations sampled with a probability proportional to the energy of an Ising configuration on their vertices, bo…
Scaling limit of triangulations of polygons
Marie Albenque, Nina Holden, Xin Sun
We prove that random triangulations of types I, II, and III with a simple boundary under the critical Boltzmann weight converge in the scaling limit to the Brownian disk. The proof…
Convergence of odd-angulations via symmetrization of labeled trees
Louigi Addario-Berry, Marie Albenque
Fix an odd integer integer. Let be a uniform -angulation with vertices and endowed with the uniform probability measure on its vertices. We prove that, there…