Methods of free probability
Probability
2024-08-30 v5 Mathematical Physics
Combinatorics
math.MP
Quantum Algebra
Abstract
This is a joint introduction to classical and free probability, which are twin sisters. We first review the foundations of classical probability, notably with the main limiting theorems (CLT, CCLT, PLT, CPLT), and with a look into examples coming from Lie groups and random matrices. Then we present the foundations and main results of free probability, notably with free limiting theorems, and with a look into examples coming from quantum groups and random matrices. We discuss then a number of more advanced aspects, in relation with free geometry and with subfactor theory.
Keywords
Cite
@article{arxiv.2208.07515,
title = {Methods of free probability},
author = {Teo Banica},
journal= {arXiv preprint arXiv:2208.07515},
year = {2024}
}
Comments
400 pages. arXiv admin note: text overlap with arXiv:2208.03600