Glauber dynamics of the FK percolation and new bound on the critical point for q<1
Date(s) : 20/01/2026 iCal
14h30 - 15h30
The FK percolation model is a variant of classical percolation, in which, in addition to the weight $p$ on the edges, a weight $q$ is added to the clusters.
When $q < 1$, the invalidity of the FKG inequalities makes it difficult to study the phase diagram. For example, on the square lattice, for $q < 1$ the model is only known to be subcritical (respectively supercritical) when $p\leq q/(1+q)$ (resp. $p\geq 1/2). These bounds comes from stochastic comparison of the model with Bernoulli percolation.
In a joint work with Vincent Beffara and Tejas Oke, we slightly extend these two regions, by improving the classical stochastic comparisons. It yields a new bound for the critical point, assuming that it exists.
The proof relies on a modification of the usual Glauber dynamics of the model, which enables stochastic bounds of FK measures between two inhomegenous percolations. We also prove uniqueness of the infinite-volume measure in our extended ranges.
Emplacement
I2M Saint-Charles - Salle de séminaire
Catégories
