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
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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. 
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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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