The normalized Perron eigenvector of exp(kA) converges to a point in the tropical max-plus eigenspace, and two conjectures locate that point from the shape of the eigenspace.
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Tropical Analysis of the Asymptotics of the Perron-Frobenius Eigenvector
The normalized Perron eigenvector of exp(kA) converges to a point in the tropical max-plus eigenspace, and two conjectures locate that point from the shape of the eigenspace.