• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - No thumbnail

Random walk driven by simple exclusion process

Huveneers, François; Simenhaus, François (2015), Random walk driven by simple exclusion process, Electronic Journal of Probability, 20, p. 42 p.. 10.1214/EJP.v20-3906

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1404.4187v3
Date
2015
Journal name
Electronic Journal of Probability
Volume
20
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
Published in
Paris
Pages
42 p.
Publication identifier
10.1214/EJP.v20-3906
Metadata
Show full item record
Author(s)
Huveneers, François
Simenhaus, François
Abstract (EN)
We prove strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter γ. First we establish that, if the asymptotic velocity of the walker is non-zero in the limiting case "γ=∞" where the environment gets fully refreshed between each step, then, for γ large enough, the walker still has a non-zero asymptotic velocity in the same direction. Second we establish that if the walker is transient in the limiting case γ=0, then, for γ small enough but positive, the walker has a non-zero asymptotic velocity in the direction of the transience. These two limiting velocities can sometimes be of opposite sign. In all cases, we show that fluctuations are normal.
Subjects / Keywords
Random walk in dynamic random environment; limit theorem; renormalization; renewal times

Related items

Showing items related by title and author.

  • Thumbnail
    A limit theorem for the survival probability of a simple random walk among power-law renewal traps 
    Poisat, Julien; Simenhaus, François (2018) Document de travail / Working paper
  • Thumbnail
    A limit theorem for the survival probability of a simple random walk among power-law renewal obstacles 
    Poisat, Julien; Simenhaus, François (2020) Article accepté pour publication ou publié
  • Thumbnail
    Localization of a one-dimensional simple random walk among power-law renewal obstacles 
    Poisat, Julien; Simenhaus, François (2022) Document de travail / Working paper
  • Thumbnail
    Random Walk on a Perturbation of the Infinitely-Fast Mixing Interchange Process 
    Salvi, Michele; Simenhaus, François (2018) Article accepté pour publication ou publié
  • Thumbnail
    Asymptotic direction for random walks in random environments 
    Simenhaus, François (2007) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo