Asymptotics of visibility in the hyperbolic plane
Artikel i vetenskaplig tidskrift, 2013

At each point of a Poisson point process of intensity λ in the hyperbolic place, center a ball of bounded random radius. Consider the probability Pr that from a fixed point, there is some direction in which one can reach distance r without hitting any ball. It is known that if λ is strictly smaller than a critical intensity λgv then Pr does not go to 0 as r→∞. The main result in this note shows that in the case λ=λgv, the probability of reaching distance larger than r decays essentially polynomial, while if λ>λgv, the decay is exponential. We also extend these results to various related models.


Pierre Calka

Advances in Applied Probability

0001-8678 (ISSN) 1475-6064 (eISSN)

Vol. 45 2 332-350


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