2 problems

All-moments critical-point conjecture. For every $W>W_c$, the martingale $(\psi_n)_{n\geq 0}$ converges in $L^p$ for every $p>1$; equivalently,

Let $d\geq 3$, let $W_c(\mathbb{Z}^d)$ denote the critical point for the vertex reinforced jump process (VRJP) on $\mathbb{Z}^d$, and let $(\psi_n)_{n\geq 0}$ be its martingale. Th…