Variations on quantum de Finetti theorems and operator valued Martin boundaries: a Choquet-Deny approach
Operator Algebras
2025-08-19 v3 Mathematical Physics
math.MP
Abstract
We revisit the quantum de Finetti theorem. We state and prove a couple of variants thereof. In parallel, we introduce an operator version of the Martin boundary on quantum groups and prove generalizations of Biane's theoresm. Our proof of the de Finetti theorem is new in the sense that it is based on an analogy with the theory of operator valued Martin boundary that we introduce.
Keywords
Cite
@article{arxiv.2402.09713,
title = {Variations on quantum de Finetti theorems and operator valued Martin boundaries: a Choquet-Deny approach},
author = {Benoît Collins and Thierry Giordano and Ryosuke Sato},
journal= {arXiv preprint arXiv:2402.09713},
year = {2025}
}
Comments
Accepted for publication in the Proceedings of the American Mathematical Society