Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Projections of probability distributions: A measure-theoretic Dvoretzky
  theorem   Many authors have studied the phenomenon of typically Gaussian marginals of
high-dimensional random vectors; e.g., for a probability measure on $\R^d$,
under mild conditions, most one-dimensional marginals are approximately
Gaussian if $d$ is large. In earlier work, the author used entropy techniques
and Stein's method to show that this phenomenon persists in the
bounded-Lipschitz distance for $k$-dimensional marginals of $d$-dimensional
distributions, if $k=o(\sqrt{\log(d)})$. In this paper, a somewhat different
approach is used to show that the phenomenon persists if
$k<\frac{2\log(d)}{\log(\log(d))}$, and that this estimate is best possible.

33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat