Appears in collection : Matrix Models for Quantum Systems – Special Day of the Seed Seminar of Mathematics and Physics

The Quantum Symmetric Simple Exclusion Process (QSSEP) is a model of quantum particles hopping on a finite interval and satisfying the exclusion principle. I will explain how free cumulants, which are quantities arising in free probability and random matrix theory, encode the fluctuations of the invariant measure of this process when the number of sites goes to infinity.