Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Volume Doubling Condition and a Local Poincar\'e Inequality on
  Unweighted Random Geometric Graphs   The aim of this paper is to establish two fundamental measure-metric
properties of particular random geometric graphs. We consider
$\varepsilon$-neighborhood graphs whose vertices are drawn independently and
identically distributed from a common distribution defined on a regular
submanifold of $\mathbb{R}^K$. We show that a volume doubling condition (VD)
and local Poincar\'e inequality (LPI) hold for the random geometric graph (with
high probability, and uniformly over all shortest path distance balls in a
certain radius range) under suitable regularity conditions of the underlying
submanifold and the sampling distribution.

14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph