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 
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/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] Yu. A. Alpin, V. S. Alpina, “Kombinatornye i spektralnye svoistva polugrupp stokhasticheskikh matrits”, Zap. nauchn. semin. POMI, 439, 2015, 13–25

[2] Yu. A. Alpin, V. S. Alpina, “Novoe dokazatelstvo teoremy Protasova–Voinova o polugruppakh neotritsatelnykh matrits”, Mat. zametki, 105:6 (2019), 807–815 | DOI | Zbl

[3] R. Stenli, Perechislitelnaya kombinatorika, Mir, M., 1990

[4] T. E. Hall, M. V. Sapir, “Idempotents, regular elements and sequences from finite semigroups”, Discrete Math., 161 (1996), 151–160 | DOI | MR | Zbl

[5] A. Paz, Introduction to Probabilistic Automata, Academic Press, New York–London, 1971 | MR | Zbl

[6] A. Paz, “Definite and quasidefinite sets of stochasic matrices”, Proc. Amer. Math. Soc., 16:4 (1965), 634–641 | DOI | MR | Zbl

[7] V. Yu. Protasov, A. S. Voynov, “Sets of nonnegative matrices without positive products”, Linear Algebra Appl., 437 (2012), 749–765 | DOI | MR | Zbl

[8] E. Seneta, Non-Negative Matrices and Markov Chains, Springer, New York, 2006 | MR | Zbl