Glauber dynamics of the FK percolation and new bound on the critical point for q<1Oberseminar Stochastics

by Corentin Faipeur (ENS Lyon)

Thursday Nov 20, 2025, 4:30 PM → 5:30 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

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, in dimension 2 with q ≥ 1, we know exactly
for which values of p and q the model admits a phase transition, and the value
of the critical point is known. For q < 1, the best bounds on the critical point
are given by comparison inequalities, which state a stochastic domination of
the model by product measures.
In a joint work with Vincent Beffara and Tejas Oke, we slightly improve these
comparison inequalities to extend the known regime of uniqueness and im-
prove the bounds on pc. To do this, we introduce the Glauber dynamics of the
model and certain local approximations, which will give a stochastic domina-
tion of the model by an inhomogeneous product measure.