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Abstract: We investigate random interlacements on Z^d, d bigger or equal to 3.
Thismodel recently introduced in arXiv:0704.2560 corresponds to a Poisson cloud onthe space of doubly infinite trajectories modulo time-shift tending to infinityat positive and negative infinite times.
A non-negative parameter u measureshow many trajectories enter the picture.
Our main interest lies in thepercolative properties of the vacant set left by random interlacements at levelu.
We show that for all d bigger or equal to 3 the vacant set at level upercolates when u is small.
This solves an open problem of arXiv:0704.2560,where this fact has only been established when d is bigger or equal to 7.
Italso completes the proof of the non-degeneracy in all dimensions d bigger orequal to 3 of the critical parameter introduced in arXiv:0704.2560.



Author: Vladas Sidoravicius, Alain-Sol Sznitman

Source: https://arxiv.org/



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