Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparse recovery properties of discrete random matrices   Motivated by problems from compressed sensing, we determine the threshold
behavior of a random $n\times d$ $\pm 1$ matrix $M_{n,d}$ with respect to the
property "every $s$ columns are linearly independent". In particular, we show
that for every $0<\delta <1$ and $s=(1-\delta)n$, if $d\leq
n^{1+1/2(1-\delta)-o(1)}$ then whp every $s$ columns of $M_{n,d}$ are linearly
independent, and if $d\geq n^{1+1/2(1-\delta)+o(1)}$ then whp there are some
$s$ linearly dependent columns.

36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th