Marie Albenque (Paris Cit茅)
Title: Sign clusters in the Infinite-Ising weighted triangulations.
Abstract: In this talk, I will survey some recent results about Ising-decorated triangulations.听In this model, triangulations are sampled together with a spin configuration on their vertices (i.e. a 2-coloring of its vertices), with a probability biased by the number of monochromatic edges, via a parameter nu. The fact that there exists a critical value for this model has been initially established in the physics literature by Kazakov and was rederived by combinatorial methods by Bousquet-Me虂lou and Schaeffer, and Bouttier, Di Francesco and Guitter.
In this talk, I will give geometric evidence that this model undergoes a phase transition by studying its monochromatic clusters. In particular, we establish that, when nu is critical or subcritical, the cluster of the root is finite almost surely, and is infinite with positive probability for nu supercritical.
This is based on joint works with Laurent M茅nard and with Laurent M茅nard and Gilles Schaeffer.
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