Probability Theory and Related Fields

, Volume 165, Issue 3–4, pp 795–834 | Cite as

Local trapping for elliptic random walks in random environments in \(\mathbb {Z}^d\)

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Abstract

We consider elliptic random walks in i.i.d. random environments on \(\mathbb {Z}^d\). The main goal of this paper is to study under which ellipticity conditions local trapping occurs. Our main result is to exhibit an ellipticity criterion for ballistic behavior which extends previously known results. We also show that if the annealed expected exit time of a unit hypercube is infinite then the walk has zero asymptotic velocity.

Keywords

Random walk in random environments Ballisticity Ellipticity 

Mathematics Subject Classification

Primary 60K37 Secondary 82D30 
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Notes

Acknowledgments

We would like to thank Alejandro Ramírez for useful discussions. The authors are also grateful to the Université de Toulouse, which they were both affiliated to at the time when this work was done.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Université de MontréalMontrealCanada
  2. 2.Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland

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