## Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments.(English)Zbl 1351.60132

Authors’ abstract: In this work, we discuss certain ballistic random walks in random environments on $$\mathbb{Z}^{d}$$, and prove the equivalence between the static and dynamic points of view in dimension $$d\geq 4$$. Using this equivalence, we also prove a version of a local limit theorem which relates the local behaviour of the quenched and annealed measures of the random walk by a prefactor.

### MSC:

 60K37 Processes in random environments 60G50 Sums of independent random variables; random walks 60F05 Central limit and other weak theorems 82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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### References:

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