Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the variance of the square components of a normal multivariate
  within a Euclidean ball   We present arguments in favour of the inequalities $var(X_n^2|X \in
B_v(\rho)) \le 2\lambda_n E[X_n^2|X \in B_v(\rho)]$, where $X \sim
N_v(0,\Lambda)$ is a normal vector in $v\ge 1$ dimensions, with zero mean and
covariance matrix $\Lambda = \diag(\lambda)$, and $B_v(\rho)$ is a centered
$v$-dimensional Euclidean ball of square radius $\rho$. Such relations lie at
the heart of an iterative algorithm, proposed in ref. [1] to perform a
reconstruction of $\Lambda$ from the covariance matrix of $X$ conditioned to
$B_v(\rho)$. In the regime of strong truncation, i.e. for $\rho \lesssim
\lambda_n$, the above inequality is easily proved, whereas it becomes harder
for $\rho \gg \lambda_n$. Here, we expand both sides in a function series
controlled by powers of $\lambda_n/\rho$ and show that the coefficient
functions of the series fulfill the inequality order by order if $\rho$ is
sufficiently large. The intermediate region remains at present an open
challenge.

37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th