Some rigorous results on the phase transition of finitary random interlacements

Abstract

In this paper, we show several rigorous results on the phase transition of Finitary Random Interlacements (FRI). For the high intensity regime, we show the existence of a critical fiber length, and find its exact asymptotic 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.