4 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…

Let $W_n$ be the polymer martingale and define … Under the assumption that the weights are bounded, the weak-disorder region is the region where $W_\infty>0$ almost surely, and…

Weak-disorder moment conjecture. For all $\delta\in(0,1)$ and $\hat\beta\in(0,1)$, uniformly for all $q<(1-\delta)q_\star(N,\hat\beta)$, as $N\to\infty$,