# Products of irreducible random matrices in the (max,+) algebra

Abstract : We consider the recursive equation x(n+1)=A(n)x(n)'' where x(n+1) and x(n) are column vectors of size k and where A(n) is an irreducible random matrix of size k x k. The matrix-vector multiplication in the (max,+) algebra is defined by (A(n)x(n))_i= max_j [ A(n)_{ij} +x(n)_j ]. This type of equation can be used to represent the evolution of Stochastic Event Graphs which include cyclic Jackson Networks, some manufacturing models and models with general blocking (such as Kanban). Let us assume that the sequence (A(n))_n is i.i.d or more generally stationary and ergodic. The main result of the paper states that the system couples in finite time with a unique stationary regime if and only if there exists a set of matrices C such that P { A(0) in C } > 0, and the matrices in C have a unique periodic regime.
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Article dans une revue
Advances in Applied Probability, Applied Probability Trust, 1997, 29 (2), pp.444-477
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Littérature citée [33 références]

https://hal.inria.fr/inria-00074735
Contributeur : Jean Mairesse <>
Soumis le : mardi 24 juillet 2007 - 18:13:46
Dernière modification le : samedi 27 janvier 2018 - 01:31:22
Document(s) archivé(s) le : mardi 21 septembre 2010 - 13:56:05

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• HAL Id : inria-00074735, version 2
• ARXIV : 0707.3672

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Jean Mairesse. Products of irreducible random matrices in the (max,+) algebra. Advances in Applied Probability, Applied Probability Trust, 1997, 29 (2), pp.444-477. 〈inria-00074735v2〉

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