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Random Walk on the Torus and Random Interlacements

  • Alexander Drewitz
  • Balázs Ráth
  • Artëm Sapozhnikov
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter we consider simple random walk on the discrete torus \(\mathbb{T}_{N}^{d}:= {(\mathbb{Z}/N\mathbb{Z})}^{d}\), d ≥ 3. We prove that for every u > 0, the local limit (as N) of the set of vertices in \(\mathbb{T}_{N}^{d}\) visited by the random walk up to time uN d steps is given by random interlacements at level u.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Alexander Drewitz
    • 1
  • Balázs Ráth
    • 2
  • Artëm Sapozhnikov
    • 3
  1. 1.Department of MathematicsColumbia UniversityNew York CityUSA
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.Max-Planck Institute of Mathematics in the SciencesLeipzigGermany

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