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Random Walk on the Torus and Random Interlacements

  • Alexander Drewitz
  • Balázs Ráth
  • Artëm Sapozhnikov
Chapter
  • 687 Downloads
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.

Keywords

Random Interlacements Lazy Random Walk Local Limit Walking Changes Sznitman 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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