# Asymptotics of the Perron Eigenvalue and Eigenvector Using Max-Algebra

Abstract : We consider the asymptotics of the Perron eigenvalue and eigenvector of irreducible nonnegative matrices whose entries have a geometric dependance in a large parameter. The first term of the asymptotic expansion of these spectral elements is solution of a spectral problem in a semifield of jets, which generalizes the max-algebra. We state a «Perron-Frobenius theorem» in this semifield, which allows us to characterize the first term of this expansion in some non-singular cases. The general case involves an aggregation procedure à la Wentzell-Freidlin.
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• HAL Id : inria-00073240, version 1

### Citation

Marianne Akian, Ravindra Bapat, Stéphane Gaubert. Asymptotics of the Perron Eigenvalue and Eigenvector Using Max-Algebra. [Research Report] RR-3450, INRIA. 1998. ⟨inria-00073240⟩

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