2 problems

The critical-threshold conjecture. The supremum is attained in the limit $t,s\to0$ with $t\ne s$, and

Let $X(u)$ be a Gaussian random field, and let $X_{\mathrm{max}}=\max_{u\in M}X(u)$. Write $\mathbb{P}_{\mathrm{tube}}(X_{\mathrm{max}}>c)$ for the tube-method approximation to…