3 problems

Let $\Phi$ have Hermite rank three or higher, and consider the random corrector $u_\varepsilon-\bar{u}$ in the long-range random potential setting described in the paper. Hermite-p…

Extension conjecture. The special SRD and LRD mixed-case limit theorem holds without the restriction that $k_{j,L}$ be $1$ or $2$; in particular,

Universality conjecture. This asymptotic normality should also occur for Hermite processes of higher order $q\geq 3$, and the threshold $H=3/4$ should be universal.