On the exact orders of critical value in Finitary Random Interlacements

Zhenhao Cai and Yuan Zhang

Stochastic Processes and their Applications, 2023, vol. 159, issue C, 391-427

Abstract: In this paper, we prove the exact orders of critical intensity u∗(T) in Finitary Random Interlacements (FRI) in Zd,d≥3 with respect to the expected fiber length T. We show that as T→∞, u∗(T) is of the same order as fd(T), where fd(T)=T−1/2,d=3T−1logT,d=4T−1,d≥5. Our estimates also give the order of magnitude at which the percolative phase transition with respect to T takes place.

Date: 2023
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DOI: 10.1016/j.spa.2023.02.008

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