Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On construction and analysis of sparse random matrices and expander
  graphs with applications to compressed sensing   We revisit the probabilistic construction of sparse random matrices where
each column has a fixed number of nonzeros whose row indices are drawn
uniformly at random. These matrices have a one-to-one correspondence with the
adjacency matrices of lossless expander graphs. We present tail bounds on the
probability that the cardinality of the set of neighbors for these graphs will
be less than the expected value. The bounds are derived through the analysis of
collisions in unions of sets using a {\em dyadic splitting} technique. This
analysis led to the derivation of better constants that allow for quantitative
theorems on existence of lossless expander graphs and hence the sparse random
matrices we consider and also quantitative compressed sensing sampling theorems
when using sparse non mean-zero measurement matrices.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex