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Two-dimensional random interlacements and late points for random walks

Abstract : We define the model of two-dimensional random interlacements us-ing the simple random walk trajectories conditioned on never hitting the origin, and then obtain some properties of this model. Also, for the random walk on a large torus conditioned on not hitting the origin up to some time proportional to the mean cover time, we show that the law of the vacant set around the origin is close to that of random interlacements at the corresponding level. Thus, this new model pro-vides a microscopic description of late points of the covering process.
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Contributor : Francis Comets <>
Submitted on : Friday, February 13, 2015 - 3:07:59 PM
Last modification on : Friday, March 27, 2020 - 4:00:24 AM
Document(s) archivé(s) le : Thursday, May 28, 2015 - 2:40:56 PM


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  • HAL Id : hal-01116486, version 1
  • ARXIV : 1502.03470


Francis Comets, Serguei Popov, Marina Vachkovskaia. Two-dimensional random interlacements and late points for random walks. 2015. ⟨hal-01116486⟩



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