On (Non-)Monotonicity and Phase Diagram of Finitary Random Interlacement

In this paper, we study the evolution of a Finitary Random Interlacement (FRI) with respect to expected length each fiber. contrast previously proved phase transition between sufficiently large and small fiber length, for all d≥3, FRI is NOT stochastically monotone as increases. At same time, numerical evidence still strongly supports existence uniqueness critical which estimated theoretically numerically be an inversely proportional function system intensity.