3 problems

Higher-dimensional extremal conjecture.

Let $d$ and $r$ be parameters of the $r$-neighbour bootstrap percolation model on the box $[n]^d$, let $p_c([n]^d,r)$ be its critical probability, let $\lambda(d,r)$ be the model-d…

Let ${\mathfrak{S}}$ be a set of small steps in $\mathbb{Z}^d$ for some dimension $d$, and let $R$ be an open region in $\mathbb{Z}^d$ bounded by rational hyperplanes. Define … Her…