Invariance principle for the random conductance model with dynamic bounded conductances

被引：20
|
作者：
Andres, Sebastian [1 ]
机构：
[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2014年 / 50卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Random conductance model; Dynamic environment; Invariance principle; Ergodic; Corrector; Point of view of the particle; Stochastic interface model; PHI INTERFACE MODEL; TIME RANDOM ENVIRONMENT; RANDOM-WALK; PERCOLATION CLUSTERS; LIMIT-THEOREM; FUNCTIONALS;
D O I：
10.1214/12-AIHP527
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We study a continuous time random walk X in an environment of dynamic random conductances in Z(d). We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for X, and obtain Green's functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.
引用
收藏
页码：352 / 374
页数：23
相关论文
共 50 条
  • [1] INVARIANCE PRINCIPLE FOR THE RANDOM CONDUCTANCE MODEL WITH UNBOUNDED CONDUCTANCES
    Barlow, M. T.
    Deuschel, J-D.
    ANNALS OF PROBABILITY, 2010, 38 (01): : 234 - 276
  • [2] Invariance principle for the random conductance model
    S. Andres
    M. T. Barlow
    J.-D. Deuschel
    B. M. Hambly
    Probability Theory and Related Fields, 2013, 156 : 535 - 580
  • [3] Invariance principle for the random conductance model
    Andres, S.
    Barlow, M. T.
    Deuschel, J. -D.
    Hambly, B. M.
    PROBABILITY THEORY AND RELATED FIELDS, 2013, 156 (3-4) : 535 - 580
  • [4] INVARIANCE PRINCIPLE FOR THE RANDOM CONDUCTANCE MODEL IN A DEGENERATE ERGODIC ENVIRONMENT
    Andres, Sebastian
    Deuschel, Jean-Dominique
    Slowik, Martin
    ANNALS OF PROBABILITY, 2015, 43 (04): : 1866 - 1891
  • [5] QUENCHED INVARIANCE PRINCIPLE FOR RANDOM WALKS AMONG RANDOM DEGENERATE CONDUCTANCES
    Bella, Peter
    Schaffner, Mathias
    ANNALS OF PROBABILITY, 2020, 48 (01): : 296 - 316
  • [6] An invariance principle for one-dimensional random walks among dynamical random conductances
    Biskup, Marek
    ELECTRONIC JOURNAL OF PROBABILITY, 2019, 24
  • [7] Quenched invariance principle for a long-range random walk with unbounded conductances
    Zhang, Zhongyang
    Zhang, Lixin
    ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2013, 10 (02): : 921 - 952
  • [8] The quenched invariance principle for random walks in random environments admitting a bounded cycle representation
    Deuschel, Jean-Dominique
    Koesters, Holger
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2008, 44 (03): : 574 - 591
  • [9] Quenched Invariance Principles for Random Walks with Random Conductances
    P. Mathieu
    Journal of Statistical Physics, 2008, 130 : 1025 - 1046
  • [10] Quenched invariance principles for random walks with random conductances
    Mathieu, P.
    JOURNAL OF STATISTICAL PHYSICS, 2008, 130 (05) : 1025 - 1046
12345