2011/06/30 by Marco Lenci
Mathematics · #Absolute continuity #Applied mathematics #Combinatorics #Continuous-time stochastic process #Discrete mathematics #Ergodic theory #Ergodicity #Interacting particle system #Invariance principle #Invariant (physics) #Invariant measure #Markov Chains and Monte Carlo Methods #Martingale (probability theory) #Mathematical Dynamics and Fractals #Mathematical physics #Mathematics #Particle system #Physics #Point process #Pure mathematics #Random walk #Statistical physics #Statistics #Stochastic process #Stochastic processes and statistical mechanics #Transitive relation #math.DS #math.PR #msc:37A20 #msc:37A50 #msc:60F17 #msc:60G42 #msc:60G50 #msc:60K37
paper · pdf · doi:10.1016/j.spa.2013.01.007
published as Stochastic Process. Appl. 123 (2013), no. 5, 1750-1764 · Final version for Stochastic Process. Appl., 18 pages, 1 figure
openalex publication_date 2013/01/16 · arxiv created 2013/01/26 · arxiv updated 2013/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider random walks in random environments on Zd. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments, we prove the ergodicity of the annealed process w.r.t. the dynamics "from the point of view of the particle". This implies in particular that the environment viewed from the particle is ergodic. As an example of application of this result, we give a general form of the quenched Invariance Principle for walks in doubly stochastic environments with zero local drift (martingale condition).