Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Error estimates for spectral convergence of the graph Laplacian on
  random geometric graphs towards the Laplace--Beltrami operator   We study the convergence of the graph Laplacian of a random geometric graph
generated by an i.i.d. sample from a $m$-dimensional submanifold $M$ in $R^d$
as the sample size $n$ increases and the neighborhood size $h$ tends to zero.
We show that eigenvalues and eigenvectors of the graph Laplacian converge with
a rate of $O\Big(\big(\frac{\log n}{n}\big)^\frac{1}{2m}\Big)$ to the
eigenvalues and eigenfunctions of the weighted Laplace-Beltrami operator of
$M$.
  No information on the submanifold $M$ is needed in the construction of the
graph or the "out-of-sample extension" of the eigenvectors. Of independent
interest is a generalization of the rate of convergence of empirical measures
on submanifolds in $R^d$ in infinity transportation distance.

19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org