Low-temperature entropy in JT gravity

For ensembles of Hamiltonians that fall under the Dyson classification of random matrices with beta is an element of {1, 2, 4}, the low-temperature mean entropy can be shown to vanish as < S(T)>similar to kappa T beta+1. A similar relation holds for Altland-Zirnbauer ensembles. JT gravity has been shown to be dual to the double-scaling limit of a beta = 2 ensemble, with a classical eigenvalue density proportional to e(S0) root E when 0 < E << 1. We use universal results about the distribution of the smallest eigenvalues in such ensembles to calculate kappa up to corrections that we argue are doubly exponentially small in S-0.

Automated summary

The study examines the relationship between entropy and temperature in ensembles of specific types of random matrices, as well as the correspondence between JT gravity and the double-scaling limit.