Work

Variations on quantum de Finetti theorems and operator valued Martin boundaries: A Choquet–Deny approach

Year: 2026

Type: article

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 theorem. 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.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17486

Authors: Benoît Collins, Thierry Giordano, Ryosuke Sato

Institutions: Kyoto University, University of Ottawa, Hokkaido University

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Natural Sciences and Engineering Research Council of Canada, Japan Society for the Promotion of Science