2 problems

Let $Q_n$ be the $n$-dimensional hypercube, let $p\in (\frac{1}{2},1]$ be fixed, and let $\mathcal{M}_{1,\geq p}(Q_n)$ denote the $1$-independent percolation measures on $Q_n$ whos…

For $d\geq 3$, let $p_{1,c}(\mathbb{Z}^d)$ denote the critical probability for $1$-independent percolation on the integer lattice. High-dimensional percolation conjecture. There ex…