Year: 2002
Type: preprint
Abstract: We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a central limit theorem for ordered joint distributions together with a commutator estimate related to the Baker-Campbell-Hausdorff expansion. The result can be considered a generalization of Johansson's theorem on the limiting distribution of the shape of a random word in a fixed alphabet as its length goes to infinity [math.CO/9906120,math.PR/9909104].
Source: arXiv (Cornell University)
Author: Kuperberg, Greg
Institution: University of California, Davis
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Award: Quantum algebra and topology
OpenAlex ID: W2951654222