In this talk, I will discuss the statistical properties of entanglement entropy, which serves as a natural measure of quantum correlations between a subsystem and its complement. Entanglement is a defining feature of quantum theory and understanding its statistical properties has applications in many areas of physics (quantum information, statistical mechanics, condensed matter physics, black hole thermodynamics).

First, I will introduce the physical model and explain its relevance for practical applications. Second, I will explain how the statistical ensemble of quantum states can naturally be described through the methods of random matrix theory. Third and finally, I review a number of new results describing the typical properties (e.g., average, variance) of the entanglement entropy for various ensembles of quantum states (general vs. Gaussian, arbitrary vs. fixed particle number).

[based on arXiv:2112.06959 and arXiv:2103.05416]