Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A CLT in Stein's distance for generalized Wishart matrices and higher
  order tensors   We study the central limit theorem for sums of independent tensor powers,
$\frac{1}{\sqrt{d}}\sum\limits_{i=1}^d X_i^{\otimes p}$. We focus on the
high-dimensional regime where $X_i \in \mathbb{R}^n$ and $n$ may scale with
$d$. Our main result is a proposed threshold for convergence. Specifically, we
show that, under some regularity assumption, if $n^{2p-1}\gg d$, then the
normalized sum converges to a Gaussian. The results apply, among others, to
symmetric uniform log-concave measures and to product measures. This
generalizes several results found in the literature.
  Our main technique is a novel application of optimal transport to Stein's
method which accounts for the low dimensional structure which is inherent in
$X_i^{\otimes p}$.

37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat