The near-critical random bond FK-percolation model

par Émile Averous

jeudi 13 nov. 2025, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (ICJ)

FK-percolation on $Z^2$ has been extensively studied, and much is known about its qualitative behaviour at its critical point when $1\leq q\leq 4$. In a box of side length N, it is known that the model keeps its critical behaviour precisely when the parameter varies around the critical point in a window of size $W(N)$. 

In this talk, we explain what happens when the critical parameter is instead perturbed by a small random amount at each edge of $Z^2$, and show that some averaging phenomenon allows the model to stay critical in the much larger window $W(N)^{1/3}$. In the case of Bernoulli percolation, additional cancellations ensure that for any centred random perturbation, the model keeps its critical behaviour in the full plane.

Joint work with Rémy Mahfouf