Critical exponents for a three-dimensional percolation model

par Pierre-François Rodriguez

jeudi 26 nov. 2020, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (La Doua, bât. Braconnier)

We consider the Gaussian free field on the cable system corresponding to a transient weighted graph and study the percolation problem associated to its excursion sets above a given real-valued height h. Owing to certain `integrability properties’ of this setup, involving the strong Markov property of the field and the central role played by a certain capacity observable, we rigorously determine the behavior of several quantities related to the (near-)critical picture for this problem. In particular, our results apply in case the base graph is the three-dimensional cubic lattice, and unveil the values of the associated critical exponents.

 

Joint work with A. Drewitz and A. Prévost.