2015/04/13 by Sascha Bachmann, Bachmann, Sascha, Giovanni Peccati +1 · 2 citations
Mathematics · #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1504.03138
We prove new concentration estimates for random variables that are\nfunctionals of a Poisson measure defined on a general measure space. Our\nresults are specifically adapted to geometric applications, and are based on a\npervasive use of a powerful logarithmic Sobolev inequality proved by L. Wu\n(2000), as well as on several variations of the so-called Herbst argument. We\nprovide several applications, in particular to edge counting and more general\nlength power functionals in random geometric graphs, as well as to the convex\ndistance for random point measures recently introduced by M. Reitzner (2013).\n