Abstract: Recently it has been shown that JT gravity is dual to a hermitian matrix model. This means that JT gravity is not dual to a single boundary theory, as we would expect from higher dimensional examples of AdS/CFT, but rather to an ensemble of theories. In this talk I will present a gravitational theory that interpolates between JT gravity, where there is an ensemble and a gravity theory with a fixed boundary Hamiltonian, which is more like what occurs in higher dimensions. For this, we consider a matrix integral with the insertion of a Gaussian with variance $\sigma$, centered around a matrix $𝖧_0$. Tightening the Gaussian renders the matrix integral less random, and ultimately it collapses the ensemble to one Hamiltonian $𝖧_0$. This model provides a concrete setup to study factorization, and what the gravity dual of a single member of the ensemble is. We find that as $\sigma$ is decreased, the JT gravity dilaton potential gets modified, and ultimately the gravity theory goes through a series of phase transitions, corresponding to a proliferation of extra macroscopic holes in the spacetime.