Introduction to the non-asymptotic analysis of random matrices
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Abstract
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of these methods sprung off from the development of geometric functional analysis in the 1970-2000's. They have applications in several fields, most notably in theoretical computer science, statistics and signal processing. A few basic applications are covered in this text, particularly for the problem of estimating covariance matrices in statistics and for validating probabilistic constructions of measurement matrices in compressed sensing. These notes are written particularly for graduate students and beginning researchers in different areas, including functional analysts, probabilists, theoretical statisticians, electrical engineers, and theoretical computer scientists.Keywords
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This publication has 45 references indexed in Scilit:
- Spectral Analysis of Large Dimensional Random Matrices2010
- Smallest singular value of a random rectangular matrixCommunications on Pure and Applied Mathematics, 2009
- On sparse reconstruction from Fourier and Gaussian measurementsCommunications on Pure and Applied Mathematics, 2007
- Random Vectors in the Isotropic PositionJournal of Functional Analysis, 1999
- Concentration of measure and isoperimetric inequalities in product spacesPublications mathématiques de l'IHÉS, 1995
- Isoperimetric problems for convex bodies and a localization lemmaDiscrete & Computational Geometry, 1995
- Majorization of Gaussian processes and geometric applicationsProbability Theory and Related Fields, 1992
- Non commutative Khintchine and Paley inequalitiesArkiv för Matematik, 1991
- On the limit of the largest eigenvalue of the large dimensional sample covariance matrixProbability Theory and Related Fields, 1988
- The eigenvalues of random symmetric matricesCombinatorica, 1981