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arXiv · 2605.30737

Reducing Kolmogorov's Reversibility Criterion Via a Basis for the Interaction Graph Kernel

Marco Antonio Cruz-dela-Rosa·Fernando Guerrero-Poblete
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Abstract

In this work, we define the interaction graph for a continuous-time Markov chain to analyze its dynamic structure. Under certain assumptions, we demonstrate that verifying Kolmogorov's reversibility criterion reduces to checking it for a cycle basis of the incidence matrix kernel associated with the interaction graph. This result provides an efficient tool for verifying reversibility in Markov continuous chains.

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Marco Antonio Cruz-dela-Rosa, Fernando Guerrero-Poblete. 2026-05-29. Reducing Kolmogorov's Reversibility Criterion Via a Basis for the Interaction Graph Kernel. https://arxiv.org/abs/2605.30737

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