Heehyun Park

The $q<1$ Random-Cluster Model on Wired Trees: Uniqueness and Negative Dependence

The random-cluster model with cluster weight $0<q<1$ is expected to exhibit negative dependence, but without FKG even pairwise negative correlation remains open on general graphs. We study the model on the infinite $\Delta$-regular tree with wired boundary conditions. Write $\widehat p:=p/(p+q(1-p))$ and $p_{\mathsf c}...