2 problems

Let $\alpha_c^{(k)}(d)$ denote the critical value of the parameter $\alpha$ for percolation in the GN$_k(d,\alpha)$ model in dimension $d$, with integer $k\geq 1$. High-dimensional…

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…