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Fernando Guerrero-Poblete

Publications and source records attributed to Fernando Guerrero-Poblete.

2 recordsLinked to original sources
arXiv2026

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

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.

math.PR↗
arXiv2026

An approach to non-equilibrium Markov chains through cycle matrices

Analogously to the quantum case considered in Cruz-de-la-Rosa and Guerrero-Poblete (Open Syst. Inf. Dyn. 32, 2550005, 2025), this work proposes a graph-theoretic approach to studying non-equilibrium properties in Markov chains. We prove that the kernel of the incidence matrix associated with the interaction graph of the chain, which consists of cycles, is isomorphic to the space of anti-symmetric matrices with rows sum to zero. The main contribution of this work is the introduction of the called cycle matrices, which constitute a basis for the space of matrices that describe the non-equilibrium.

math.PR↗