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Large Deviations for the Graph Distance in Supercritical Continuum Percolation

  • Chang-Long Yao (a1), Ge Chen (a1) and Tian-De Guo (a1)

Abstract

Denote the Palm measure of a homogeneous Poisson process H λ with two points 0 and x by P0,x . We prove that there exists a constant μ ≥ 1 such that P0,x (D(0, x) / μ||x||2 ∉ (1 − ε, 1 + ε) | 0, xC ) exponentially decreases when ||x||2 tends to ∞, where D(0, x) is the graph distance between 0 and x in the infinite component C of the random geometric graph G(H λ; 1). We derive a large deviation inequality for an asymptotic shape result. Our results have applications in many fields and especially in wireless sensor networks.

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Copyright

Corresponding author

Postal address: School of Mathematical Science, Graduate University of Chinese Academy of Sciences, 100049, Beijing, P. R. China.
∗∗ Email address: deducemath@126.com

References

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Keywords

MSC classification

Large Deviations for the Graph Distance in Supercritical Continuum Percolation

  • Chang-Long Yao (a1), Ge Chen (a1) and Tian-De Guo (a1)

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