The fun of free probability is that if you think you have seen everything in the subject suddenly new exciting connections are popping up. This happened for example a few months ago with the preprints
Eigenstate Thermalization Hypothesis and Free Probability, by Silvia Pappalardi, Laura Foini, and Jorge Kurchan
Dynamics of Fluctuations in the Open Quantum SSEP and Free Probability, by Ludwig Hruza and Denis Bernard
According to the authors, the occurrence of free probability in both problems has a similar origin: the coarse-graining at microscopic either spatial or energy scales, and the unitary invariance at these microscopic scales. Thus the use of free probability tools promises to be ubiquitous in chaotic or noisy many-body quantum systems.
I still have to have a closer look on these connections and thus I am very excited that there will be great opportunity for learning more about this (and other connections) and discussing it with the authors at a special day at IHP, Paris on 25 January 2023. This is part of a two-day conference “Inhomogeneous Random Structures”.
Wednesday 25 January: Free probability, between maths and physics.
Moderator: Jorge Kurchan (Paris)
Free probability is a flourishing field in probability theory. It deals with non-commutative random variables where one introduces the concept of «freeness» in analogy to «independence» of commuting random variables. On the mathematical side, it has given new tools and a deeper insight into, amongst others, the field of random matrices. On the physics side, it has recently appeared naturally in the context of quantum chaos, where all its implications have not yet been fully worked out.
Speakers: Denis Bernard (Paris), Jean-Philippe Bouchaud (Paris), Laura Foini (Saclay), Alice Guionnet (Lyon), Frederic Patras (Nice), Marc Potters (Paris), Roland Speicher (Saarbrücken)