Discrete max-plus spectral theory

By Marianne Akian, Stephane Gaubert, Cormac Walsh. 2004

68 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/55a2627b9c0302a6d9d9b1626c63d382c1408421

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In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

The max-plus Martin boundary (2004, background): “all the circuits of the graph of A. The existence of a super-harmonic row vector with full support, Assumption 2.2, implies that ρ(A) ≤ (see for instance Prop. 3.5 of [Dud92] or Lemma 2.2 of [ AGW05 ]).”
On visualization scaling, subeigenvectors and Kleene stars in max algebra (2008, unknown): “For a more recent reference, see generalization of the max-plus spectral theory [1], where they are called super-eigenvectors.”
The Maslov dequantization, idempotent and tropical mathematics: A brief introduction (2005, background): “t [17]; see also a ﬁnite dimensional version of the separation theorem in [133]. Three papers on this subject by M. Akian, S. Gaubert, V. Kolokoltsov, G. Cohen, J.-P. Quadrat, I. Singer, and C. Walsh [3,5,18] arepublished in this volume. There is an “idempotent” version of the theory of linear repre”
Max-Plus Algebra (2006, background): “See [BCOQ92] and [AGW05] for more accessible accounts.”