Distinct critical diffusion constants conjecture

Fix $n\geq 1$. For each $p$, let $\kappa_p^{(n)}$ denote the critical diffusion constant associated with $p$-intermittency. Distinct critical values conjecture. For all fixed $n\geq 1$ and sufficiently large spatial dimension $d$, the critical values $\kappa_p^{(n)}$ are pairwise distinct. This conjecture concerns the separation of the transitions between different intermittency regimes. It is presented as an analogue of a conjecture for the white-noise potential; only partial results for that analogue are cited, and the assertion here remains open in the supplied source.