6 problems

Fix irrational $\kappa\in(0,8)$ and let $\mathrm{LP}(n,m)$ be the set of link patterns. Let $\mathcal{Z}_{\alpha}$ be the pure partition function indexed by…

Fekete–Pommerenke energy conjecture.

Let $\hat\beta_{\mathrm{eff}}$ be the effective inverse temperature defined in the source, and let $f^{\operatorname{Coul}}(\beta)$, $f^{\operatorname{IV}}(\beta^{-1})$,…

Let $(\beta_n)$ be a sequence of inverse temperatures, and consider the Coulomb gas configurations at these temperatures. Sharpness conjecture. If almost sure uniform separation ho…

Strong beta-ensemble expansion conjecture.

Mabuchi energy expansion conjecture. Under these assumptions,