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

Glenn Merlet

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

Probability 2007-05-23 v3 Optimization and Control

Authors: Glenn Merlet

Abstract

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.

Keywords

random matrices max-plus algebra memory loss property discrete event systems stationary regime

Cite

@article{arxiv.math/0405452,
  title  = {Memory loss property for products of random matrices in the $(\max,+)$ algebra},
  author = {Glenn Merlet},
  journal= {arXiv preprint arXiv:math/0405452},
  year   = {2007}
}

Comments

The article has been completely rewritten, in order to state more explicit results and allow the matrices' entries to be infinite. Moreover the results are illustrated on a simple production system

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

Abstract

Keywords

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