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

Glenn Merlet (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: max-plus algebra; random matrices; DEDS

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

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⟩