3 problems

Let $\lpha_c$, $\lpha_u$, $\lpha_{\rm tr}$, and $\lpha_{\mathop{\rm b2b}}$ denote the thresholds defined in the paper for, respectively, percolation, uniqueness, truncated-model pe…

Fix $q\in(1,4)$, set $r=1/q$, and let $\omega^\delta$ be the fuzzy Potts configuration on $\delta\mathbb{Z}^2$. For lattice approximations $z_i^\delta$ of…

For $d\geq4$, consider the Brownian loop-soup in $(0,1)^d$ and the operation of contracting each loop, so that percolation can be viewed as a mechanism for gluing loops into cluste…