5 problems

Let $\mathcal{U}$ be a $d$-dimensional update family, and let $p_c(\mathbb{Z}^d,\mathcal{U})$ denote its critical probability. The family $\mathcal{U}$ is subcritical when every he…

Tang's conjecture. Both Kahn's vertex-cut characterization for $p_c^{site}(G)$ and the Lyons–Peres edge-cut characterization for $p_c^{site}(G)$ hold for site percolation on every…

Consider the standard lattice graphs for which numerical values of the Bernoulli bond percolation critical probability $p_c$ are available, and let the super-kagome lattice be the…

Let $G$ be an infinite, connected, transitive, simple graph of vertex degree $d$ that is not one-dimensional, and let $p_c(G)$ be its Bernoulli bond percolation critical probabilit…

Let $\mathcal U_d^*$ be the class of infinite unimodular transitive graphs of degree $d$ that are not one-dimensional. For a graph $G$ with origin $o$, let $B_n$ be the radius-$n$…