Critical exponents for a percolation model on transient graphs

03.10.2022 16:15 – 18:15

I will present some conjectures about critical exponents for percolation models with long-range correlations, and explain how these conjectures are solved in the specific case of level sets percolation for the Gaussian free field on the cable system. An essential role will be played by a certain capacity functional of the level sets, which appear naturally in a differential formula associated with this model. In particular, one can explicitly compute the law of the capacity of bounded clusters, and deduce asymptotics for various quantities in the critical or near-critical regime, such as the percolation probability or two points function. The talk is based on joint work with Alexander Drewitz and Pierre-François Rodriguez.

Lieu

Salle 1-15, Séminaire "Maths-Physique"

entrée libre