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

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

2004-05-24

arxiv.org/abs/math/0405452v3

Mathematics

Probability

The article has been completely rewritten, in order to state more explicit results and allow the matrices' entries to be infin

Scientific paper

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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