Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments

Noam Berger ^[1] ; Moran Cohen ^[1] ; Ron Rosenthal ^[2]
1. [1] Hebrew University of Jerusalem
  
  Hebrew University of Jerusalem
  
  Israel
2. [2] Swiss Federal Institute of Technology in Zurich
  
  Swiss Federal Institute of Technology in Zurich
  
  Zürich, Suiza
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 4, 2016, págs. 2889-2979
Idioma: inglés
DOI: 10.1214/15-AOP1038
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Resumen
- In this work, we discuss certain ballistic random walks in random environments on ZdZd, and prove the equivalence between the static and dynamic points of view in dimension d≥4d≥4. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor.