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A Markov chain representation of the Perron-Frobenius eigenvector
Raphaël Cerf, Joseba Dalmau · 2016-07-05 · via math.PR updates on arXiv.org

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 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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