Discrete max-plus spectral theory

2004/05/12 by Marianne Akian, Stephane Gaubert, Cormac Walsh
Mathematics · #math.SP #math.OC #msc:47J10 #msc:49L20 #msc:15A48

paper · pdf

published as Appears in "Idempotent Mathematics and Mathematical Physics", G.L. Litvinov and V.P. Maslov, Eds, vol. 377 of Contemporary Mathematics, pp. 53--77, AMS, 2005. · 25 pages, 7 figures. ESI preprint

arxiv created 2004/05/12 · arxiv updated 2009/12/01

Abstract

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.

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