Quantum Gravity as a Multitrace Matrix Model

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from two dimensions and captures a large class of spaces admiting a finite spectral triple. These multitrace matrix models sustain emergent geometry as well as growing dimensions and topology change.