The partition functions of Jackiw–Teitelboim (JT) gravity corresponds to random matrix integral. And we can define three different versions of bosonic JT gravity which are dual to matrix integrals of GUE, GOE, and GSE, respectively. In fact, the largest eigenvalue
$$\lambda_{\textrm{max}}$$
of the Gaussian unitary random matrix GUE is described by the Tracy–Widom distribution. Then we show that there is a third-order order phase transition in the JT gravity as
$$\lambda_{\textrm{max}}$$
crosses its mean value from left w...
