Discrete max-plus spectral theory

Marianne Akian (1) , Stéphane Gaubert (1) , Cormac Walsh (1)

1 MAXPLUS - Max-plus algebras and mathematics of decision

We develop a max-plus spectral theory for infinite matrices. We introduce recurrence and tightness conditions, under which many results of the finite dimensional theory, concerning the representation of eigenvectors and the asymptotic behavior of powers of matrices, carry over. We also announce more general representation results for eigenvectors, which are obtained by introducing a max-plus analogue of the Martin boundary.

Domaines: Théorie spectrale [math.SP]; Optimisation et contrôle [math.OC]

Marianne Akian, Stéphane Gaubert, Cormac Walsh. Discrete max-plus spectral theory. G.L. Litvinov and V.P. Maslov. Idempotent Mathematics and Mathematical Physics, 377 (377), American Mathematical Society, pp.53--77, 2005, Contemporary Mathematics. ⟨inria-00000968⟩