One-dimensional finite range random walk in random medium and invariant measure equation

Julien Brémont

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 1, page 70-103
  • ISSN: 0246-0203

Abstract

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We consider a model of random walks on ℤ with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce a characterization of the non-zero-speed regime of the model.

How to cite

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Brémont, Julien. "One-dimensional finite range random walk in random medium and invariant measure equation." Annales de l'I.H.P. Probabilités et statistiques 45.1 (2009): 70-103. <http://eudml.org/doc/78022>.

@article{Brémont2009,
abstract = {We consider a model of random walks on ℤ with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce a characterization of the non-zero-speed regime of the model.},
author = {Brémont, Julien},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {finite range Markov chain; Lyapunov eigenvector; invariant measure; stable cone},
language = {eng},
number = {1},
pages = {70-103},
publisher = {Gauthier-Villars},
title = {One-dimensional finite range random walk in random medium and invariant measure equation},
url = {http://eudml.org/doc/78022},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Brémont, Julien
TI - One-dimensional finite range random walk in random medium and invariant measure equation
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 1
SP - 70
EP - 103
AB - We consider a model of random walks on ℤ with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce a characterization of the non-zero-speed regime of the model.
LA - eng
KW - finite range Markov chain; Lyapunov eigenvector; invariant measure; stable cone
UR - http://eudml.org/doc/78022
ER -

References

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