Random Matrix Models, 2D Quantum Gravity, and Holography (Part 1)

 In the first of two lectures I will present a pedagogical exploration of perhaps the simplest random matrix model, the Gaussian Unitary Ensemble. It gives the Airy model in the double scaling limit. I will first review the features that we usually focus on when studying models of gravity and argue that they need to be supplemented by much more non-perturbative information, readily computed using Fredholm determinants. The physical picture that emerges implies a specific kind of discrete spectrum, apparently previously unnoticed in this context. Its holographic meaning is discussed. This all readily generalizes to an infinite family of models.