Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polylog dimensional subspaces of $\ell_\infty^N$   We show that a subspace of of $\ell_\infty^N$ of dimension $n>(\log N\log
\log N)^2$ contains $2$-isomorphic copies of $\ell_\infty^k$ where $k$ tends to
infinity with $n/(\log N\log \log N)^2$. More precisely, for every $\eta>0$, we
show that any subspace of $\ell_\infty^N$ of dimension $n$ contains a subspace
of dimension $m=c(\eta)\sqrt{n}/(\log N\log \log N)$ of distance at most
$1+\eta$ from $\ell_\infty^m$.

36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga