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Two-dimensional random interlacements: 0-1 law and the vacant set at criticality

Author

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  • Collin, Orphée
  • Popov, Serguei

Abstract

We correct and streamline the proof of the fact that, at the critical point α=1, the vacant set of the two-dimensional random interlacements is infinite (Comets and Popov, 2017). Also, we prove a zero–one law for a natural class of tail events related to the random interlacements.

Suggested Citation

  • Collin, Orphée & Popov, Serguei, 2024. "Two-dimensional random interlacements: 0-1 law and the vacant set at criticality," Stochastic Processes and their Applications, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:spapps:v:169:y:2024:i:c:s0304414923002442
    DOI: 10.1016/j.spa.2023.104272
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