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

Replaced by

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.

Reference

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