A Markov chain representation of the Perron-Frobenius eigenvector
Probability
2017-04-26 v3 Populations and Evolution
Abstract
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.
Keywords
Cite
@article{arxiv.1607.01127,
title = {A Markov chain representation of the Perron-Frobenius eigenvector},
author = {Raphaël Cerf and Joseba Dalmau},
journal= {arXiv preprint arXiv:1607.01127},
year = {2017}
}