Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Majorizing measures and proportional subsets of bounded orthonormal
  systems   In this article we prove that for any orthonormal system $(\vphi_j)_{j=1}^n
\subset L_2$ that is bounded in $L_{\infty}$, and any $1 < k <n$, there exists
a subset $I$ of cardinality greater than $n-k$ such that on $\spa\{\vphi_i\}_{i
\in I}$, the $L_1$ norm and the $L_2$ norm are equivalent up to a factor $\mu
(\log \mu)^{5/2}$, where $\mu = \sqrt{n/k} \sqrt{\log k}$. The proof is based
on a new estimate of the supremum of an empirical process on the unit ball of a
Banach space with a good modulus of convexity, via the use of majorizing
measures.

8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci