Large deviations for the graph distance in supercritical continuum percolation
Yao, Chang-Long ; Chen, Ge ; Guo, Tian-De
J. Appl. Probab., Tome 48 (2011) no. 1, p. 154-172 / Harvested from Project Euclid
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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, x ∈ C∞) 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.
Publié le : 2011-03-15
Classification:  Continuum percolation,  chemical distance,  shape theorem,  large deviation inequality,  60K35,  82B43 
@article{1300198142,
     author = {Yao, Chang-Long and Chen, Ge and Guo, Tian-De},
     title = {Large deviations for the graph distance in supercritical continuum percolation},
     journal = {J. Appl. Probab.},
     volume = {48},
     number = {1},
     year = {2011},
     pages = { 154-172},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1300198142}
}

Yao, Chang-Long; Chen, Ge; Guo, Tian-De. Large deviations for the graph distance in supercritical continuum percolation. J. Appl. Probab., Tome 48 (2011) no. 1, pp.  154-172. http://gdmltest.u-ga.fr/item/1300198142/