Some Rigorous Results on the Phase Transition of Finitary Random Interlacement

2021/01/20 by Zhenhao Cai, Yuan Zhang, Cai, Zhenhao +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.2101.08010

arxiv created 2021/01/20 · openalex publication_date 2021/01/20 · arxiv updated 2021/01/21 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we show several rigorous results on the phase transition of Finitary Random Interlacement (FRI). For the high intensity regime, we show the existence of a critical fiber length, and give the exact asymptotic of it as intensity goes to infinity. At the same time, our result for the low intensity regime proves the global existence of a non-trivial phase transition with respect to the system intensity.

Citations

• Percolation for the Finitary Random interlacements

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

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