Entanglement Entropies of Eigenstates of Many-Body Systems and Random Matrices

I will consider eigenstates of chaotic many-body quantum systems and of a class of random matrices designed to mimic some behaviors of many-body systems (power-law-banded random matrices). I will focus on the entropy of entanglement between two halves of the system, and describe the properties of eigenstate entanglement entropies in different parts of the spectrum.