In this survey article, we give an introduction to two methods of proof in random matrix theory: The method moments and the Stieltjes transform method. We thoroughly develop these apply them show both semicircle law Marchenko-Pastur for matrices with independent entries. material is presented a pedagogical manner suitable anyone who has followed course measure-theoretic probability theory.

the focus of this paper is to consider the compressed sensing problem. it is stated that the compressed sensing theory, under certain conditions, helps relax the nyquist sampling theory and takes smaller samples. one of the important tasks in this theory is to carefully design measurement matrix (sampling operator). most existing methods in the literature attempt to optimize a randomly initiali...

We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where space possible Dirac operators is assigned a probability distribution. These ensembles are constructed as toy Euclidean quantum gravity on finite spaces and display many interesting properties. The exhibit phase transitions, near these transiti...