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On the Helmholtz decomposition for finite Markov processes

Author

Listed:
  • Laurent Miclo

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique)

Abstract

Helmholtz decompositions break down any vector field into a sum of a gradient field and a divergence-free vector field. Such a result is extended to finite irreducible and reversible Markov processes, where vector fields cor-respond to anti-symmetric functions on the oriented edges of the underlying graph.

Suggested Citation

  • Laurent Miclo, 2024. "On the Helmholtz decomposition for finite Markov processes," Working Papers hal-04472425, HAL.
  • Handle: RePEc:hal:wpaper:hal-04472425
    Note: View the original document on HAL open archive server: https://hal.science/hal-04472425
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