4 problems

Critical KPZ scaling-limit conjecture. There exists a non-random function $b(\varepsilon)>0$ with $b(\varepsilon)\to\infty$ as $\varepsilon\to0$ such that, for every…

Let $d\geq 3$, and let $(\beta_{L^N})_{N\geq 2}$ denote the critical coupling constants associated with the $N$-th moments of the stochastic heat equation. Strict-ordering conjectu…

Let the two-dimensional critical stochastic heat flow be the flow of random measures on $\mathbb R^2$ constructed as the scaling limit of intermediate-disorder directed-polymer par…

Spatial asymptotic conjecture. In the particular case of space-time white noise,