Quenched invariance principle for random walks with time-dependent ergodic degenerate weights

• Sebastian Andres ^[1] ; Alberto Chiarini ^[3] ; Jean-Dominique Deuschel ^[2] ; Martin Slowik ^[2]
  1. [1] University of Cambridge

     University of Cambridge

     Cambridge District, Reino Unido

     
  2. [2] Technical University of Berlin

     Technical University of Berlin

     Berlin, Stadt, Alemania

     
  3. [3] Aix-Marseille Université (France)

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 46, Nº. 1, 2018, págs. 302-336
• Idioma: inglés
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• Resumen

  • We study a continuous-time random walk, XX, on ZdZd in an environment of dynamic random conductances taking values in (0,∞)(0,∞). We assume that the law of the conductances is ergodic with respect to space–time shifts. We prove a quenched invariance principle for the Markov process XX under some moment conditions on the environment. The key result on the sublinearity of the corrector is obtained by Moser’s iteration scheme.