LOCAL LIMIT THEOREM AND EQUIVALENCE OF DYNAMIC AND STATIC POINTS OF VIEW FOR CERTAIN BALLISTIC RANDOM WALKS IN I.I.D. ENVIRONMENTS

LOCAL LIMIT THEOREM AND EQUIVALENCE OF DYNAMIC AND STATIC POINTS OF VIEW FOR CERTAIN BALLISTIC RANDOM WALKS IN I.I.D. ENVIRONMENTS

In this work, we discuss certain ballistic random walks in random environments on ℤd, and prove the equivalence between the static and dynamic points of view in dimension d ≥ 4. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched...

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Veröffentlicht in:The Annals of probability 2016-07, Vol.44 (4), p.2889-2979
Hauptverfasser: Berger, Noam, Cohen, Moran, Rosenthal, Ron
Format: Artikel
Sprache:eng
Schlagworte:
Ballistics
Cubes
Ellipticity
Hyperplanes
Infinity
Mathematical analysis
Polynomials
Random variables
Random walk
Random walk theory
Studies
Theorems
Triangle inequalities
Velocity
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Zusammenfassung:In this work, we discuss certain ballistic random walks in random environments on ℤd, and prove the equivalence between the static and dynamic points of view in dimension d ≥ 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.
ISSN:0091-1798
2168-894X
DOI:10.1214/15-AOP1038