Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Error of Random Sampling: Uniformly Distributed Random Points on
  Parametric Curves   Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$,
how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such
a way that it is distributed uniformly with respect to the arc-length?
Unfortunately, we cannot sample exactly such a point-even assuming we can
perform exact arithmetic operations. So we end up with the following question:
how does the method we choose affect the quality of the approximate sample we
obtain? In practice, there are many answers. However, in theory, there are
still gaps in our understanding. In this paper, we address this question from
the point of view of complexity theory, providing bounds in terms of the size
of the desired error.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc