On the Helmholtz decomposition for finite Markov processes

Résumé

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.

Remplacé par

Laurent Miclo, « On the Helmholtz decomposition for finite Markov processes », Séminaire de Probabilités, vol. 2363, mars 2025, p. 263–292dans Séminaire de Probabilités LII: Lecture Notes in Mathematics, sous la direction de Catherine Donati-Martin, Antoine Lejay et Alain Rouault, Springer Cham, vol. 2363, mars 2025, p. 263–292.