5 problems

Let $\mathcal M^{n,t,\gamma}$ be the measure from Theorem, and let $\widehat{\mathcal M}^{n,t,\gamma}$ be the probability measure on ordered $n$-tuples of negative even integers wi…

In the three-dimensional Coulomb gas and log-gas with Euclidean confinement, let the edge refer to the outer boundary of the equilibrium particle distribution, and consider the flu…

Conjectural two-dimensional fluctuation theorem. The centered random height function, multiplied by $\sqrt{\pi}$, converges in distribution to the pullback under $\Omega$ of the Ga…

Let $\mathbb{W}$ denote the renormalized energy of an infinite configuration of points, and consider its restriction to lattice configurations in low dimensions. Crystallization co…

Let $V$ be a potential and let $\beta$ be the inverse temperature of the associated log-gas. For $\beta\notin\{1,2,4\}$, there is no natural random matrix ensemble behind this mode…