A probabilistic proof of the <scp>Perron–Frobenius</scp> theorem

The Perron–Frobenius theorem plays an important role in many areas of management science and operations research. This article provides a probabilistic perspective on the theorem, by discussing proof that exploits representation eigenvalue eigenvectors terms dynamics Markov chain. recovers conditions both finite-dimensional infinite-dimensional settings under which have been shown to exist other methods. In addition providing new insights, representations arise can be used produce Monte–Carlo algorithm for computing will explored elsewhere.