Secrecy coverage in two dimensions

Amites Sarkar
2014 2014 Information Theory and Applications Workshop (ITA)  
Let P and P be independent Poisson processes, of intensities 1 and λ respectively, in R 2 . Place an open disc D(p, rp) of radius rp around each point p ∈ P, where rp is maximal so that D(p, rp) ∩ P = ∅. We thus obtain a random set A λ ⊂ R 2 which is the union of discs centered at the points of P. Now let Bn ⊂ R 2 be a fixed disc of area n, and set A λ (Bn) = A λ ∩ Bn. Write B λ (n) for the event that A λ (Bn) covers Bn (except for the points of P ), and set p λ (n) = P(B λ (n)). Extending
more » ... n)). Extending results in [7], we show that if λ 3 n log n → ∞, then p λ (n) → 0, while if λ 3 n log n(log log n) 2 → 0, then p λ (n) → 1.
doi:10.1109/ita.2014.6804272 dblp:conf/ita/Sarkar14 fatcat:f5z44hvccff6lilfrt3pz4x55e