• (May 22, 2008) M. Rudelson, R. Vershynin, The least singular value of a random square matrix is O(n^{-1/2}), submitted. Commentary.
  
• M. Rudelson, R. Vershynin, The smallest singular value of a random rectangular matrix, submitted. Commentary. Slides
  
• D. Needell, R. Vershynin, Signal recovery from incomplete and inaccurate measurements via Regularized Orthogonal Matching Pursuit, sumbitted. Commentary
  
  Conference version: Greedy signal recovery and uncertainty principles, Computational Imaging VI, IS&T/SPIE 19th Annual Symposium, 2008. Proc. SPIE Vol. 6814, 68140J.
  
• D. Needell, R. Vershynin, Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit, Foundations of Computational Mathematics, DOI: 10.1007/s10208-008-9031-3. Commentary
• M. Rudelson, R. Vershynin, The Littlewood-Offord Problem and invertibility of random matrices, Advances in Mathematics 218 (2008), 600--633. Commentary. Slides 
• R. Vershynin, Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms. In: Banach Spaces and their applications in analysis, de Gruyter, 2007, pp. 209--218
  
• M. Rudelson, R. Vershynin, Sampling from large matrices: an approach through geometric functional analysis, Journal of the ACM (2007), Art. 21, 19 pp. Commentary
• Yu. Lyubarskii, R. Vershynin, Uncertainty principles and vector quantization, submitted. Commentary. Slides.
  
  
• A. Gilbert, M. Strauss, J. Tropp, R. Vershynin, One sketch for all: fast algorithms for compressed sensing, STOC 2007 (39th ACM Symposium on Theory of Computing), to appear
  
  
• B. Klartag, R.Vershynin, Small ball probability and Dvoretzky theorem, Israel Journal of Mathematics 157 (2007), 193--207.  Commentary
  
  
• T. Strohmer, R. Vershynin, A randomized solver for linear systems with exponential convergence, RANDOM 2006 (10th International Workshop on Randomization and Computation), Springer Lecture Notes in Computer Science 4110, 499--507. Commentary
  
  Journal version: A randomized Kaczmarz algorithm with exponential convergence, Journal of Fourier Analysis and Applications, to appear
  
  
• R. Vershynin, Beyond Hirsch Conjecture: walks on random polytopes and smoothed complexity of the simplex method, FOCS 2006 (47th Annual Symposium on Foundations of Computer Science), 133--142. Commentary
  
  (April 30, 2008) Journal version: Beyond Hirsch Conjecture: walks on random polytopes and smoothed complexity of the simplex method, submitted
• A. Gilbert, M. Strauss, J. Tropp, R. Vershynin, Algorithmic linear dimension reduction in the ell-1 norm for sparse vectors, submitted. Commentary
  
  Conference version: Algorithmic Linear Dimension Reduction in the L1 Norm for Sparse Vectors, Allerton 2006 (44th Annual Allerton Conference on Communication, Control, and Computing), invited paper.
• M. Rudelson, R.Vershynin, Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements, CISS 2006 (40th Annual Conference on Information Sciences and Systems), invited paper. Commentary
  
  Journal version: On sparse reconstruction from Fourier and Gaussian measurements, Communications on Pure and Applied Mathematics, to appear. Commentary
• R. Vershynin, Random sets of isomorphism of linear operators on Hilbert space, IMS Lecture Notes -- Monograph Series, High Dimensional Probability, Vol. 51 (2006), 148--154. Commentary
  
  
• R.Vershynin, Isoperimetry of waists and local versus global asymptotic convex geometries (with an appendix by M.Rudelson and R.Vershynin), Duke Mathematical Journal 131 (2006), 1--16  Commentary
  
  
• M. Rudelson, R.Vershynin, Combinatorics of random processes and sections of convex bodies, Annals of Mathematics 164 (2006), 603--648. Commentary and Introductory Notes
  
  
• M. Rudelson, R.Vershynin, Geometric approach to error correcting codes and reconstruction of signals, International Mathematical Research Notices 64 (2005), 4019--4041 Commentary
  
  Conference version: E. Candes, M. Rudelson, T. Tao, R. Vershynin, Error correction via Linear Programming, FOCS 2005 (46th Annual Symposium on Foundations of Computer Science), 295--308
  
  
• R.Vershynin,  Frame expansions with erasures: an approach through the non-commutative operator theory, Applied  and Computational Harmonic Analysis 18 (2005), 167--176  Commentary
  
  
• R. Vershynin, Integer cells in convex sets, Advances in Mathematics 197 (2005), 248--273
• P. G. Casazza, O. Christensen, A. M. Lindner, R. Vershynin, Frames and the Feichtinger conjecture, Proceedings of the AMS 133 (2005), 1025-1033
• A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, R. Vershynin, Euclidean embeddings in spaces of finite volume ratio via random matrices, Journal für die Reine und Angewandte Mathematik 589 (2005), 1--19
• A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, R. Vershynin, Random Euclidean embeddings in spaces of bounded volume ratio, Comptes rendus de l'Académie des sciences - Mathématique 339 (2004), 33--38
• S. Mendelson, R.Vershynin, Remarks on the geometry of coordinate projections in R^n, Israel Journal of Mathematics 140 (2004), 203--220
• S. Mendelson, R.Vershynin, Entropy and the combinatorial dimension, Inventiones Mathematicae 152 (2003), 37--55
• G. Schechtman, N. Tomczak-Jaegermann, R. Vershynin, Maximal l_p^n-structures in spaces with extremal parameters, Geometric aspects of functional analysis,  223--240, Lecture Notes in Mathematics, 1807, Springer, Berlin, 2003
• M. Rudelson, R. Vershynin, Embedding Levy families into Banach spaces, Geometric and Functional Analysis 12 (2002), 183--198
• R. Vershynin, John's decompositions: selecting a large part, Israel Journal of Mathematics 122 (2001), 253--277
• S. Mendelson, R.Vershynin, Entropy, Combinatorial dimensions and Random Averages, in: COLT 2002 (15th  Annual Conference on Computational Learning Theory), edited by J. Kivinen and R. Sloan, Springer 2002, p. 14--28
• R. Vershynin, Subsequences of frames, Studia Mathematica 145 (2001), 185--197
• R.Vershynin, On large random almost Euclidean bases, Acta Mathematica Universitatis Comenianae 69 (2000), no. 2, 137--144
• R.Vershynin, Absolutely representing systems, uniform smoothness and type, Questionae Mathematica 23 (2000), no. 1, 87--98
• R. Vershynin, On constructions of strong and uniformly minimal M-bases in Banach spaces, Arch. Math. (Basel) 74 (2000), 50--60
• R. Vershynin, Embedding of operator ranges and the reflexivity of Banach spaces (Russian), Ukrainian  Math. Journal 51 (1999), no. 2, 293--296
• R. Vershynin, On 1+epsilon_n-bounded M-bases (Russian), Russian Math. (Iz. VUZ) 43 (1999), no. 4, 22--25
• R. Vershynin, On representing and absolutely representing systems in Banach spaces (Russian), Mat. Fiz. Anal. Geom. 5 (1998), 3--14
• V. Kadets, R. Vershynin, The selection problem for bases with brackets and for strong M-bases, Rendiconti Istituto Lombardo Sez. A 131 (1997), 169--177

Unpublished:

• N. Tomczak-Jaegermann, R. Vershynin, Sizes of projections of symmetric convex bodies