On the Helmholtz decomposition for finite Markov processes

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 correspond to anti-symmetric functions on the oriented edges of the underlying graph.

Replaces

Laurent Miclo, “On the Helmholtz decomposition for finite Markov processes”, TSE Working Paper, n. 24-1504, February 2024.

Reference

Laurent Miclo, “On the Helmholtz decomposition for finite Markov processes”, Séminaire de Probabilités, vol. 2363, March 2025, p. 263–292in Séminaire de Probabilités LII: Lecture Notes in Mathematics, Catherine Donati-Martin, Antoine Lejay, and Alain Rouault (eds.), Springer Cham, vol. 2363, March 2025, p. 263–292.