Some Rigorous Results on the Phase Transition of Finitary Random Interlacement

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.

References in corpus (5)

• Phase transition and level-set percolation for the Gaussian free field
• Decoupling inequalities and interlacement percolation on G x Z
• On the internal distance in the interlacement set
• On Chemical Distance and Local Uniqueness of a Sufficiently Supercritical Finitary Random Interlacement
• Percolation for the Finitary Random interlacements

Cited by in corpus (1)

• Percolation for the Gaussian free field on the cable system: counterexamples