Geodesic
Ergodicity index of the set of stochastic matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 7-17

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The paper introduces and explores the notions of ergodicity index and ergodicity exponent of a set of stochastic matrices. For the ergodicity exponent a sharp upper bound is obtained. A particular case of this bound is the well-known Paz bound. Also a connection between the ergodicity index and the Protasov–Voynov imprimitivity index is established. 
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     title = {Ergodicity index of the set of stochastic matrices},
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}
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Yu. A. Al'pin; V. S. Al'pina. Ergodicity index of the set of stochastic matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 7-17. http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a1/