3 problems

Projected Wiener dynamics conjecture. For $T_\varepsilon\leq c\varepsilon\eta_\varepsilon^{-1}\wedge\tau$, one expects

Interface annihilation conjecture. When two interfaces in the stochastic Allen–Cahn equation become separated by a distance of order $\varepsilon$, both interfaces annihilate.

Consider an interface dynamics on $\mathbb{Z}^2$ subject to a small, uniform applied field of the form $h/N$, where $h>0$, and a nucleated droplet that grows to cover the whole spa…