Concentration for Poisson functionals: Component counts in random geometric graphs

Sascha Bachmann

Stochastic Processes and their Applications, 2016, vol. 126, issue 5, 1306-1330

Abstract: Upper bounds for the probabilities P(F≥EF+r) and P(F≤EF−r) are proved, where F is a certain component count associated with a random geometric graph built over a Poisson point process on Rd. The bounds for the upper tail decay exponentially, and the lower tail estimates even have a Gaussian decay.

Keywords: Random graphs; Component counts; Concentration inequalities; Logarithmic Sobolev inequalities; Poisson point process (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.11.004

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