Random Triangulations Coupled with an Ising Model

      Angel and Schramm proved in 2003, that uniform planar triangulations converge for the local topology. The limiting law, known as UIPT (for Uniform Infinite Planar Triangulation) has been much studied since and is now a well understood object. In this talk, we will study random triangulations with an Ising configuration sampled according to their energy and not the uniform measure. The limiting object turns out to be much harder to study than the UIPT and is believed to belong to another universality class at criticality. 
      I will first review the result of Angel and Schramm and present the general context and main open questions of this field and then will discuss our result. 
This is a joint work with Laurent Ménard and Gilles Schaeffer.