Memory loss property for products of random matrices in the (,+) algebra
Glenn Merlet
Abstract
Products of random matrices in the (,+) 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.
Create a lesson
Related papers
KPP type reaction--diffusion equations in narrow tubes with degenerating boundary and generalized second order operators
Hyejin Kim
Scaling Limits of Density Fluctuation Fields of the Symmetric Partial Exclusion Processes Approaching the Zero Range Process
Kanta Nozawa
Drift and joint minimal displacement for groups acting on hyperbolic spaces
Koji Fujiwara, Ryokichi Tanaka
Gaussian approximation for the integrated intensity of counting processes: application to Hawkes processes
Benjamin Massat
Exponential functionals of two random walks and stationary measures of discrete growth processes
Zikun Ouyang
Percolative MDLA: phase transition and critical behaviour
Eviatar B. Procaccia, Haoyu Wang, Yuan Zhang