4 problems

Let CLE be a conformal loop ensemble on the sphere, and consider loops surrounding three marked points. For each such loop, let its conformal radius about the corresponding point b…

Let $\Sigma$ be a surface and let $\phi:\Sigma\to\mathbb{R}$ denote the Liouville field, with parameters $\gamma\in(0,2)$ and $Q=\frac{\gamma}{2}+\frac{2}{\gamma}$. Primary-field c…

Dual degenerate insertion conjecture. For every real $p<\frac{4}{\gamma^2}$,

Let $\gamma\in(0,2)$, and let $Y_\gamma$ denote the random variable whose nonnegative integer moments satisfy the Fyodorov–Bouchaud identity. For a real number $p$ with…