On the exact orders of critical value in Finitary Random Interlacements

2021/12/02 by Zhenhao Cai, Yuan Zhang, Cai, Zhenhao +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.2112.01136

29 pages, 2 figures

openalex publication_date 2021/12/02 · arxiv created 2021/12/04 · arxiv updated 2021/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the exact orders of critical intensity u_*(T) in Finitary Random Interlacements (FRI) in ℤ^d, d≥ 3 with respect to the expected fiber length T. We show that as T→∞, u_*(T)∼ T^-1, d≥ 5; u_*(T)∼ T^-1log T, d=4; u_*(T)∼ T^-1/2, d=3. Our estimates also give the order of magnitude at which the percolative phase transition with respect to T takes place.

Citations

• On the range of random walk

Cited by

• Asymptotics for the percolation threshold of finitary random interlacements in four and higher dimensions

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