Geodesic
The Perron–Frobenius theorem – a proof with the use of Markov chains
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 5-16 
Yu. A. Al'pin; V. S. Al'pina. The Perron–Frobenius theorem – a proof with the use of Markov chains. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 5-16. http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a0/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The Perron–Frobenius theorem for an irreducible nonnegative matrix is proved using the matrix graph and the ergodic theorem of the theory of Markov chains. Bibl. – 7 titles.

[1] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1967 | MR

[2] H. Mink, Nonnegative Matrices, Wiley, New York etc., 1988 | MR

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

[4] V. Romanovsky, “Un théorème sur les zéros des matrices non négatives”, Bull. Soc. Math. France, 61 (1933), 213–219 | MR | Zbl

[5] V. I. Romanovskii, Diskretnye tsepi Markova, Gostekhizdat, M., 1949

[6] Dzh. Kemeni, Dzh. Snell, Konechnye tsepi Markova, Nauka, M., 1970

[7] A. N. Shiryaev, Veroyatnost-1, MTsNMO, M., 2004