2013/07/24 by Bubacarr Bah, Jared Tanner, Bah, Bubacarr +1
Computer Science · Engineering · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Random Matrices and Applications #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1307.6477
openalex publication_date 2013/07/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.