From noncommutative geometry to random matrix theory

We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where space possible Dirac operators is assigned a probability distribution. These ensembles are constructed as toy Euclidean quantum gravity on finite spaces and display many interesting properties. The exhibit phase transitions, near these transitions they show manifold-like behavior. In certain cases one can recover Liouville double scaling limit. highlight examples bootstrap techniques, Coulomb gas methods, Topological Recursion applicable.