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

Key Points

• The research aims to explore and prove variations of the quantum de Finetti theorem and introduce an operator version of the Martin boundary.
• Revisiting and proving variants of the quantum de Finetti theorem.
• Introducing an operator version of the Martin boundary on quantum groups.
• Generalizing Biane's theorem through analogy.
• New proof of the quantum de Finetti theorem emphasizing its operator connection.
• Generalizations of Biane’s theorem have been established.