Central Limit Theorem for Tensor Products of Free Variables via Bi-Free Independence
Operator Algebras
2024-05-30 v1
Abstract
In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix models, it is demonstrated that the spectral distribution of certain self-adjoint quantum channels and tensor products of random matrices tend to a distribution that can be obtained by an averaged sum of products of bi-freely independent pairs. Subsequently, using bi-free techniques, a Central Limit Theorem for such operator is established.
Keywords
Cite
@article{arxiv.2405.19216,
title = {Central Limit Theorem for Tensor Products of Free Variables via Bi-Free Independence},
author = {Paul Skoufranis},
journal= {arXiv preprint arXiv:2405.19216},
year = {2024}
}