Effective Action in Free Probability
arXiv:2305.08871 · doi:10.61102/1024-2953-mprf.2024.30.1.006
Abstract
Recent works have explored relations between classical and quantum statistical physics on the one hand and Voiculescu's theory of free probability on the other. Motivated by these results, the present work focuses on the notion of effective action, which is closely related to the large deviation rate function in classical probability and one-particle irreducible correlation functions in quantum field theories. The central aim is to understand how it can be defined and studied in free probability. In this respect, we introduce a suitable diagrammatic formalism.
References in corpus (11)
- Mastering the Master Field
- Stochastic Master Fields
- Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
- Cumulants, free cumulants and half-shuffles
- The splitting process in free probability theory
- Exact Entanglement in the Driven Quantum Symmetric Simple Exclusion Process
- Bernoulli variables, classical exclusion processes and free probability
- The combinatorics of Green's functions in planar field theories
- Free cumulants, Schröder trees, and operads
- Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability
- Monotone Cumulant-Moment Formula and Schröder Trees