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Concentration for Poisson U-statistics: Subgraph counts in random geometric graphs

Sascha Bachmann and Matthias Reitzner

Stochastic Processes and their Applications, 2018, vol. 128, issue 10, 3327-3352

Abstract: Concentration bounds for the probabilities P(N≥M+r) and P(N≤M−r) are proved, where M is a median or the expectation of a subgraph count N associated with a random geometric graph built over a Poisson process. The lower tail bounds have a Gaussian decay and the upper tail inequalities satisfy an optimality condition. A remarkable feature is that the underlying Poisson process can have a.s. infinitely many points.

Keywords: Random graphs; Subgraph counts; Concentration inequalities; Stochastic geometry; Poisson point process; Convex distance (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:eee:spapps:v:128:y:2018:i:10:p:3327-3352