In this talk, I will give a description of semi-classical gravity in terms of quantum chaos and statistical physics. I will present the OPE Randomness Hypothesis (ORH), a generalization of ETH to CFTs which treats any OPE coefficient involving a heavy operator as a pseudo-random variable with an approximate Gaussian distribution. I will then present some evidence for this conjecture, based on the size of the non-Gaussianities and on insights from random matrix theory. I will argue that semi-classical gravity describes the true microscopics, but only statistically. The statistical correlations are geometrized by wormhole geometries, which explains the factorization puzzle. Time-permitted, I will show that the non-Gaussianities of the OPE coefficients predict a new connected wormhole geometry that dominates over the genus-2 wormhole.
