6 problems

Higher-even-moment collapse conjecture. For the classes $\mathbb{E}X^{2m}\leq\kappa_{2m}$, the one-sided/two-sided collapse of the cited collapse result persists beyond the corresp…

Let $\mathcal{T}_N^{\rm be}$ and $\mathcal{T}_N^{\rm rbb}$ be the argmax locations on $[0,1]$ of the non-intersecting Brownian excursion and reflected Brownian bridge ensembles, re…

Let $\mathcal{T}$ be the limiting polymer endpoint variable, and let $t>0$. Sharp tail constant conjecture. The constant in the cubic tail asymptotic is … The source says this was…

Let $\mathcal{T}$ denote the argmax location of the Airy process with parabolic drift, and let $t>0$. Halperin–Zhang conjecture. The polymer endpoint distribution satisfies … for s…

Let $\{\xi_n\}$ be a sequence of general i.i.d. random variables, and let $\{a_n\}$ and $\{b_n\}$ be sequences satisfying suitable conditions. Conjecture. After suitable scaling, t…

Let $\mathcal{T}$ be the location of the maximizer of $\mathcal{A}_2(t)-t^2$, whose almost-sure uniqueness is established in the surrounding discussion. The notation $e^{-ct^3}$ de…