4 papers · 1 filter
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…
Percolation probability and critical exponents for site percolation on the UIPT
Laurent Ménard
We derive three critical exponents for Bernoulli site percolation on the on the Uniform Infinite Planar Triangulation (UIPT). First we compute explicitly the probability that the r…
Long induced paths in a configuration model
Nathanaël Enriquez, Gabriel Faraud, Laurent Ménard +1
In an article published in 1987 in Combinatorica \cite{MR918397}, Frieze and Jackson established a lower bound on the length of the longest induced path (and cycle) in a sparse ran…
The skeleton of the UIPT, seen from infinity
Nicolas Curien, Laurent Ménard
We prove that geodesic rays in the Uniform Infinite Planar Triangulation (UIPT) coalesce in a strong sense using the skeleton decomposition of random triangulations discovered by K…