Low-temperature entropy in JT gravity

A bstract For ensembles of Hamiltonians that fall under the Dyson classification random matrices with ? ? {1, 2, 4}, low-temperature mean entropy can be shown to vanish as ? S ( T )? ? ?T + 1 . similar relation holds for Altland-Zirnbauer ensembles. JT gravity has been dual double-scaling limit a = 2 ensemble, classical eigenvalue density $$ \propto {e}^{S_0}\sqrt{E} ? e S 0 E when 0 < E ? 1. We use universal results about distribution smallest eigenvalues in such calculate ? up corrections we argue are doubly exponentially small