4 problems

Universality conjecture. Such scaling limits should be universal for a wide class of Hermitian random matrices. This predicts that the same limiting random point fields, including…

Gibbsianness conjecture. The fermion random point field $\mu^{(J)}$ is a Gibbs measure for the specification in Proposition 1.

Johansson's conjecture. Almost surely, $H(t)$ has a unique maximum point in $[-T,T]$.

Let $u{kappa,beta,mu}$ be the distribution of the random point measure $4xi{kappa}4$ on $4mathbb{R}^d4$ for $4kappa04$, and let $4mathfrak{L}4$ denote Lebesgue measure on…