Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of circulant embedding methods for sampling stationary random
  fields   In this paper we prove, under mild conditions, that the positive definiteness
of the circulant matrix appearing in the circulant embedding method is always
guaranteed, provided the enclosing cube is sufficiently large. We examine in
detail the case of the Mat\'ern covariance, and prove (for fixed correlation
length) that, as $h_0\rightarrow 0$, positive definiteness is guaranteed when
the random field is sampled on a cube of size order $(1 + \nu^{1/2} \log
h_0^{-1})$ times larger than the size of the physical domain. (Here $h_0$ is
the mesh spacing of the regular grid and $\nu$ the Mat\'ern smoothness
parameter.) We show that the sampling cube can become smaller as the
correlation length decreases when $h_0$ and $\nu$ are fixed. Our results are
confirmed by numerical experiments. We prove several results about the decay of
the eigenvalues of the circulant matrix. These lead to the conjecture, verified
by numerical experiment, that they decay with the same rate as the
Karhunen--Lo\`{e}ve eigenvalues of the covariance operator.

25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an