Random statistics of OPE coefficients and Euclidean wormholes

We propose an ansatz for OPE coefficients in chaotic conformal field theories which generalizes the Eigenstate Thermalization Hypothesis and describes any coefficient involving heavy operators as a random variable with Gaussian distribution. In two dimensions this enables us to compute higher moments of analyse four-point functions coefficients, we relate genus-2 partition their squares. compare results our solutions Einstein gravity AdS$_3$, including Euclidean wormhole that connects surfaces. Our reproduces non-perturbative correction wormhole, giving it physical interpretation terms statistics. calculations performed within semi-classical low-energy gravitational theory are only sensitive nature explains apparent lack factorization products functions.