Matrix models for eigenstate thermalization

Understand

We develop a class of matrix models which implement and formalize the `eigenstate thermalization hypothesis' (ETH) and point out that in general these models must contain non-Gaussian corrections, already in order to correctly capture thermal mean-field theory, or to capture non-trivial OTOCs as well as their higher-order generalizations.

• We develop the framework of these `ETH matrix models', and put it in the context of recent studies in statistical physics incorporating higher statistical moments into the ETH ansatz.
• We then use the `ETH matrix model' in order to develop a matrix-integral description of JT gravity coupled to a single scalar field in the bulk.
• This particular example takes the form of a double-scaled ETH matrix model with non-Gaussian couplings matching disk correlators and the density of states of the gravitational theory.