5 problems

Critical moment blowup threshold conjecture. For all $p>0$,

Let $\lambda_p^{u_0}(\kappa)$ denote the quenched Lyapunov exponent of order $p\in\mathbb{N}$ for mobility parameter $\kappa$, and let $\lambda_0^{u_0}(\kappa)$ be the correspondin…

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…

Fix $n\in\mathbb{N}$. Let $d$ be the spatial dimension, let $\kappa\geq 0$ be the diffusion constant of the catalyst, and let $\kappa_p^{(n)}$ denote the critical values governing…

Let $\xi$ be the random potential satisfying the essential-supremum and bounded independent-identically-distributed assumptions, let $\kappa>0$ be the diffusion parameter, and let…