Random walks on discrete cylinders and random interlacements

@article{Sznitman2008RandomWO,
  title={Random walks on discrete cylinders and random interlacements},
  author={A. S. Sznitman},
  journal={Probability Theory and Related Fields},
  year={2008},
  volume={145},
  pages={143-174}
}
  • A. Sznitman
  • Published 2008
  • Mathematics, Physics
  • Probability Theory and Related Fields
AbstractWe explore some of the connections between the local picture left by the trace of simple random walk on a cylinder $${(\mathbb {Z} / N\mathbb {Z})^d \times \mathbb {Z}}$$ , d ≥ 2, running for times of order N2d and the model of random interlacements recently introduced in Sznitman ( http://www.math.ethz.ch/u/sznitman/preprints). In particular, we show that for large N in the neighborhood of a point of the cylinder with vertical component of order Nd the complement of the set of points… Expand
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We introduce a model of random interlacements made of a countable collection of doubly infinite paths on Z^d, d bigger or equal to 3. A non-negative parameter u measures how many trajectories enterExpand
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