4 problems

Let $d\geq 1$, and let $J:\mathbb{Z}^d\times\mathbb{Z}^d\to[0,\infty)$ be a symmetric, integrable, translation-invariant kernel. Suppose that there are constants $0<\alpha<d$ and…

Let ${\cal W}_{k}(L)$ be the nested-path correlation function for a two-dimensional critical percolation model of linear size $L$, and let $X_{\textsc{mnp}}(k)$ denote the monochro…

The twisted amplitude conjecture. The amplitude is

The amplitude conjecture. The amplitude is