Memory loss property for products of random matrices in the $(\max,+)$ algebra
| dc.creator | Merlet, Glenn | |
| dc.date | 2004-05-24 | |
| dc.date | 2007-01-08 | |
| dc.date.accessioned | 2026-07-07T07:38:47Z | |
| dc.date.available | 2026-07-07T07:38:47Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/0405452 | |
| dc.identifier | http://arxiv.org/abs/math/0405452 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121220 | |
| dc.subject | Probability | |
| dc.subject | Optimization and Control | |
| dc.subject | 93C65;93B25;68R10;15A52 | |
| dc.title | Memory loss property for products of random matrices in the $(\max,+)$ algebra | |
| dc.type | text |