Memory loss property for products of random matrices in the $(\max,+)$ algebra - Archive ouverte HAL
Article Dans Une Revue Mathematics of Operations Research Année : 2010

Memory loss property for products of random matrices in the $(\max,+)$ algebra

Glenn Merlet

Résumé

Products of random matrices in the $(\max,+)$ algebra are used as a model for a class of discrete event dynamical systems. J. Mairesse proved that such a system couples in finite times with a unique stationary regime if and only if it has a memory loss property. We prove that the memory loss property is generic in the following sense : if it is not fulfilled, the support of the measure is included in a finite union of affine hyperplanes and in the discrete case the atoms of the measure are linearly related.
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Dates et versions

hal-00001607 , version 1 (24-05-2004)
hal-00001607 , version 2 (08-04-2005)
hal-00001607 , version 3 (08-01-2007)

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Glenn Merlet. Memory loss property for products of random matrices in the $(\max,+)$ algebra. Mathematics of Operations Research, 2010, ⟨10.1287/moor.1090.0434⟩. ⟨hal-00001607v3⟩
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