Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating the inverse of banded matrices by banded matrices with
  applications to probability and statistics   In the first part of this paper we give an elementary proof of the fact that
if an infinite matrix $A$, which is invertible as a bounded operator on
$\ell^2$, can be uniformly approximated by banded matrices then so can the
inverse of $A$. We give explicit formulas for the banded approximations of
$A^{-1}$ as well as bounds on their accuracy and speed of convergence in terms
of their band-width. In the second part we apply these results to covariance
matrices $\Sigma$ of Gaussian processes and study mixing and beta mixing of
processes in terms of properties of $\Sigma$. Finally, we note some
applications of our results to statistics.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn