Kemeny's constant minimization for reversible Markov chains via structure-preserving perturbations

Fabio Durastante; Miryam Gnazzo; Beatrice Meini

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arXiv · 2510.24679

Kemeny's constant minimization for reversible Markov chains via structure-preserving perturbations

Fabio Durastante·Miryam Gnazzo·Beatrice Meini

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Abstract

Kemeny's constant measures the efficiency of a Markov chain in traversing its states. We investigate whether structure-preserving perturbations to the transition probabilities of a reversible Markov chain can improve its connectivity while maintaining a fixed stationary distribution. Although the minimum achievable value for Kemeny's constant can be estimated, the required perturbations may be infeasible. We reformulate the problem as an optimization task, focusing on solution existence and efficient algorithms, with an emphasis on the problem of minimizing Kemeny's constant under sparsity constraints.

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Fabio Durastante, Miryam Gnazzo, Beatrice Meini. 2025-10-28. Kemeny's constant minimization for reversible Markov chains via structure-preserving perturbations. https://arxiv.org/abs/2510.24679

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