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A category-theoretic proof of the ergodic decomposition theorem

Abstract:

The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms of string diagrams, using the formalism of Markov categories. We recover the usual measure-theoretic statement by instantiating our result in the category of stochastic kernels. Along the way we give a conceptual treatment of several concepts in the theory o...

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Publication status:
Accepted
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Computer Science
Role:
Author
ORCID:
0000-0002-9123-9089
Publisher:
Cambridge University Press Publisher's website
Journal:
Ergodic Theory and Dynamical Systems Journal website
Acceptance date:
2023-01-16
EISSN:
1469-4417
ISSN:
0143-3857
Language:
English
Keywords:
Pubs id:
1324818
Local pid:
pubs:1324818
Deposit date:
2023-01-22

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