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March 2011 Large deviations for the graph distance in supercritical continuum percolation
Chang-Long Yao, Ge Chen, Tian-De Guo
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J. Appl. Probab. 48(1): 154-172 (March 2011). DOI: 10.1239/jap/1300198142

Abstract

Denote the Palm measure of a homogeneous Poisson process Hλ 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(Hλ; 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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Chang-Long Yao. Ge Chen. Tian-De Guo. "Large deviations for the graph distance in supercritical continuum percolation." J. Appl. Probab. 48 (1) 154 - 172, March 2011. https://doi.org/10.1239/jap/1300198142

Information

Published: March 2011
First available in Project Euclid: 15 March 2011

zbMATH: 1213.60161
MathSciNet: MR2809893
Digital Object Identifier: 10.1239/jap/1300198142

Subjects:
Primary: 60K35
Secondary: 82B43

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 1 • March 2011
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