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In Entropy (Basel, Switzerland)

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

Cai Zhenhao, Xiong Yunfeng, Zhang Yuan


critical value, finitary random interlacement, percolation phase transition