5 problems

Universal Type I conjecture. The model $I(G,p)$ is of Type $\mathcal{I}$ for every initial density $p\in(0,1)$.

Let $G$ be a quasi-transitive graph. Let $p_h$ denote the critical probability for the regime in which Bernoulli percolation clusters have infinite total weight, and let $p_u$ deno…

Bernoulli percolation uniqueness conjecture. Bernoulli percolation with $p$ sufficiently close to $1$ should have a unique infinite cluster, so that

Let $G$ be a quasi-transitive locally finite connected graph. A process of splittings repeatedly factors any factor with more than one end, and stops when all factors have at most…

Finite termination conjecture. Every process of splittings must end after finitely many steps.