5 problems

Positive critical regrowth conjecture. The critical regrowth parameter is positive:

Stochastic differential approximation conjecture. The process $\mathcal{X}_n$ behaves like a continuous-time process $X_t$ satisfying

Let $\nu$ be the infinite-volume sandpile measure and let $\mathrm{rad}(\mathrm{Av}_o)$ be the radius of the avalanche set generated by adding a particle at the origin. Avalanche-r…

Let $\nu$ be the infinite-volume sandpile measure. For an avalanche started by adding a particle at the origin, let $S_o=\sum_{x\in\mathbb{Z}^d}n(o,x;\cdot)$ be the total number of…

Let $\nu$ be the infinite-volume sandpile measure on $\{0,1,\ldots,2d-1\}^{\mathbb{Z}^d}$, let $\mathrm{Av}_o=\{x\in\mathbb{Z}^d:n(o,x;\cdot)>0\}$ be the avalanche set generated by…