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arXiv · 2606.24584

On the convergence of doubly stochastic Markov chains

Ludovick Bouthat·Nicolas Doyon·Javad Mashreghi·Frédéric Morneau-Guérin
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Abstract

We characterize the asymptotic behavior of time-homogeneous doubly stochastic Markov chains. Our investigation revolves around understanding the dynamics of products of doubly stochastic matrices, which in turn allows us to fully characterize three distinct behaviors: cyclicity, convergence towards a special equilibrium matrix, and divergence. Notably, we introduce a novel and comprehensive sufficient condition for the convergence of an infinite product of doubly stochastic matrices.

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Ludovick Bouthat, Nicolas Doyon, Javad Mashreghi, Frédéric Morneau-Guérin. 2026-06-23. On the convergence of doubly stochastic Markov chains. https://doi.org/10.5565/publmat7022606

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