5 problems

Let $\Gamma_s^\epsilon$ be the set of right-most infinite open paths at dynamical time $s$. Let $S_{\alpha(p),\sigma(p),\epsilon}$ denote the corresponding space-time rescaling, an…

Barrier-cone characterization conjecture. For every $p\in[0,1]$,

Consider sufficiently spread-out oriented percolation in dimension $d>4$, with spread parameter $L$ sufficiently large, and let $\mathcal {T}_n$ denote the set of vertices connecte…

For $0 \leq p \leq 1$, let $\vec{\mathbb{Z}}^2(p)$ be the random orientation of the square lattice in which each horizontal edge is oriented rightwards with probability $p$ and lef…

Oriented-percolation critical crossing summability conjecture.