Visibility in Brownain interlacements, Poisson cylinders and Boolean models

2023/04/20 by Mu, Yingxin, Sapozhnikov, Artem
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2304.10298

Abstract

We study visibility inside the vacant set of three models in \mathbb R^d with slow decay of spatial correlations: Brownian interlacements, Poisson cylinders and Boolean model. For each of them, we obtain sharp asymptotic bounds on the probability of visibility to distance r in some direction in terms of the probability of visibility to distance r in a given direction. In dimensions d≥ 4, the ratio of the two probabilities has the same scaling r^2(d-1) for all three models, but in lower dimensions the scalings are different. In particular, we improve some main results from arXiv:0905.4874 and arXiv:1709.09052.

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