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.For the proof of the concentration inequalities, recently developed methods based on logarithmic Sobolev inequalities are used and enhanced. A particular advantage of this approach is that the resulting inequalities even apply in settings where the underlying Poisson process has infinite intensity measure.
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