nLab de Finetti's theorem

Idea

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Motivation

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In measure-theoretic probability

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In Markov categories

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Quantum versions

(For now, see the references.)

See also

• probability theory, categorical probability
• infinitary tensor product, Kolmogorov extension theorem
• Giry monad, probability monad, Markov category
• exchangeability?, limit

References

• Bart Jacobs, Sam Staton, De Finetti’s construction as a categorical limit, Proceedings of CMCS, 2021. (arXiv:2003.01964)

• Tobias Fritz, Tomáš Gonda, Paolo Perrone, De Finetti’s theorem in categorical probability. Journal of Stochastic Analysis, 2021. (arXiv:2105.02639)

• Sean Moss, Paolo Perrone, Probability monads with submonads of deterministic states, LICS 2022. (arXiv:2204.07003)

• Tobias Fritz, Tomáš Gonda, Paolo Perrone, Eigil Fjeldgren Rischel, Representable Markov categories and comparison of statistical experiments in categorical probability, Theoretical Computer Science 961, 2023. (arXiv:2010.07416)

• Noé Ensarguet, Paolo Perrone, Categorical probability spaces, ergodic decompositions, and transitions to equilibrium, arXiv:2310.04267

For the quantum case:

• Sam Staton and Ned Summers, Quantum de Finetti Theorems as Categorical Limits, and Limits of State Spaces of $C^\ast$-algebras, Proceedings of Quantum Physics and Logic, 2022. (arXiv)

• Tobias Fritz and Antonio Lorenzin, Involutive Markov categories and the quantum de Finetti theorem, 2023. (arXiv)

category: probability