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math.PR2018
Galton-Watson and branching process representations of the normalized Perron-Frobenius eigenvector
Raphaël Cerf, Joseba Dalmau
Let be a primitive matrix and let be its Perron-Frobenius eigenvalue. We give formulas expressing the associated normalized Perron-Frobenius eigenvector as a simple functio…
math.PR2018
A probabilistic proof of Perron's theorem
Raphaël Cerf, Joseba Dalmau
We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of…