Ergodic decompositions of Dirichlet forms under order isomorphisms

2021/09/01 by Lorenzo Dello Schiavo, Melchior Wirth · 1 voice · 3 citations
Mathematics · #Advanced Topology and Set Theory #Combinatorics #Computer science #Dirichlet distribution #Dirichlet form #Ergodic theory #Geometric and Algebraic Topology #Isomorphism (crystallography) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Order (exchange) #Pure mathematics #Space (punctuation) #Unitary state #math.FA #math.PR

paper · pdf · doi:10.1007/s00028-022-00859-7

published in Journal of Evolution Equations 23(1), 9 (Birkhäuser)

arxiv published 2021/09/01 · openalex created_date 2021/09/13 · arxiv updated 2022/11/27 · openalex publication_date 2022/12/30 · openalex updated_date 2026/08/05

Abstract

We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces.

Citations

• Classical Descriptive Set Theory
• Can One Hear the Shape of a Drum?
• The Dirichlet-Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold
• Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications
• Can One Hear the Shape of a Drum?

Discussions

• AUTOMATIC REPOST OF OLD TWEETS FROM TWITTER (X) FOR ARCHIVING PURPOSES [27.09.2021] --- New preprint on "Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms" by L. Dello Schiavo and M. [bsky, 0 points, 0 comments]

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