Open Access
2017 A Markov chain representation of the normalized Perron–Frobenius eigenvector
Raphaël Cerf, Joseba Dalmau
Electron. Commun. Probab. 22: 1-6 (2017). DOI: 10.1214/17-ECP76


We consider the problem of finding the Perron–Frobenius eigenvector of a primitive matrix. Dividing each of the rows of the matrix by the sum of the elements in the row, the resulting new matrix is stochastic. We give a formula for the normalized Perron–Frobenius eigenvector of the original matrix, in terms of a realization of the Markov chain defined by the associated stochastic matrix. This formula is a generalization of the classical formula for the invariant probability measure of a Markov chain.


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Raphaël Cerf. Joseba Dalmau. "A Markov chain representation of the normalized Perron–Frobenius eigenvector." Electron. Commun. Probab. 22 1 - 6, 2017.


Received: 23 February 2017; Accepted: 20 July 2017; Published: 2017
First available in Project Euclid: 13 October 2017

zbMATH: 1373.15016
MathSciNet: MR3718702
Digital Object Identifier: 10.1214/17-ECP76

Primary: 15A18‎ , 60J10

Keywords: eigenvector , Markov chain , Perron Frobenius

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