Quantum Exclusion Process, Random Matrices and Free Cumulants

Explore the intricacies of the Quantum Symmetric Simple Exclusion Process (QSSEP) in this illuminating lecture. Delve into the model of quantum particles hopping on a finite interval while adhering to the exclusion principle. Discover how free cumulants, originating from free probability and random matrix theory, encode the fluctuations of the invariant measure as the number of sites approaches infinity. Gain insights from Philippe Biane of the Laboratoire d'Informatique Gaspard Monge in Marne-la-Vallée as he elucidates the connections between quantum processes, random matrices, and free cumulants in this hour-long presentation from the Institut des Hautes Etudes Scientifiques (IHES).