On the Helmholtz decomposition for finite Markov processes

Laurent Miclo ()
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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

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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.

Keywords: Helmholtz decompositions; Compact Riemannian manifolds; Vector fields; Gradient fields; Poisson equation; Optimal transport; Finite Markov processes; Finite weighted graphs (search for similar items in EconPapers)
Date: 2024-02-22
Note: View the original document on HAL open archive server: https://hal.science/hal-04472425v1
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