Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concentration for Poisson functionals: component counts in random
  geometric graphs   Upper bounds for the probabilities $\mathbb{P}(F\geq \mathbb{E} F + r)$ and
$\mathbb{P}(F\leq \mathbb{E} F - r)$ are proved, where $F$ is a certain
component count associated with a random geometric graph built over a Poisson
point process on $\mathbb{R}^d$. 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.

37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin